diff --git a/02-basic-python/02-basic-python-in-class.ipynb b/02-basic-python/02-basic-python-in-class.ipynb index 1bee6b3..91b3877 100644 --- a/02-basic-python/02-basic-python-in-class.ipynb +++ b/02-basic-python/02-basic-python-in-class.ipynb @@ -859,9 +859,9 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "Python [conda env:base] *", "language": "python", - "name": "python3" + "name": "conda-base-py" }, "language_info": { "codemirror_mode": { @@ -873,7 +873,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.13.5" + "version": "3.13.9" } }, "nbformat": 4, diff --git a/02-basic-python/02-basic-python.ipynb b/02-basic-python/02-basic-python.ipynb index 3f302c8..ef33e44 100644 --- a/02-basic-python/02-basic-python.ipynb +++ b/02-basic-python/02-basic-python.ipynb @@ -89,7 +89,9 @@ }, { "cell_type": "markdown", - "metadata": {}, + "metadata": { + "jp-MarkdownHeadingCollapsed": true + }, "source": [ "## Jupyter Notebook Basics\n", "\n", @@ -234,14 +236,32 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "pycharm": { "is_executing": false }, "scrolled": true }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hello World!\n" + ] + }, + { + "data": { + "text/plain": [ + "3" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "print (\"Hello World!\")\n", "a = 3\n", @@ -265,7 +285,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "pycharm": { "is_executing": false @@ -274,7 +294,7 @@ "outputs": [], "source": [ "age = 2\n", - "gender = \"woman\"\n", + "gender = \"female\"\n", "name = \"Datascience Cat\"\n", "smart = True" ] @@ -292,9 +312,17 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Datascience Cat, age: 2, female, is smart: True\n" + ] + } + ], "source": [ "print(name + \", age: \" + str(age) + \", \" + \n", " gender + \", is smart: \" + str(smart))" @@ -311,9 +339,20 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Datascience Cat \n", + " age: 2 \n", + " female \n", + " is smart: True\n" + ] + } + ], "source": [ "print(name, \"\\n\",\n", " \"age:\", age, \"\\n\",\n", @@ -339,6 +378,28 @@ "3. Modify the above print statement to add your UID and email to the print-out." ] }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "uID: u146792 \n", + " email: hadleyblackwell05@gmail.com\n" + ] + } + ], + "source": [ + "uID = \"u146792\"\n", + "email = \"hadleyblackwell05@gmail.com\"\n", + "\n", + "print(\"uID: \", uID, \"\\n\",\n", + " \"email: \", email)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -530,9 +591,17 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Within function: only readable in here\n" + ] + } + ], "source": [ "def scope_test():\n", " function_scope = \"only readable in here\"\n", @@ -554,11 +623,12 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 25, "metadata": {}, "outputs": [], "source": [ - "print(\"Outside function: \" + function_scope)" + "# print(\"Outside function: \" + function_scope)\n", + "# supressed output since incorrect" ] }, { @@ -574,9 +644,17 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Dr. Science Cat\n" + ] + } + ], "source": [ "name = \"Science Cat\"\n", "\n", @@ -595,9 +673,17 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Dr. Science Cat\n" + ] + } + ], "source": [ "# note that we're re-using the parameter name defined in the previous cell.\n", "def print_name_with_dr(name):\n", @@ -615,9 +701,18 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Within function: defined in the function, global scope\n", + "Outside function: defined in the function, global scope\n" + ] + } + ], "source": [ "def scope_test():\n", " # Think long and hard before you do this - generally you shouldn't. I have never.\n", @@ -646,6 +741,45 @@ "3. When you try each function, what is the result? What is the value of the `x` outside the function?" ] }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "the result of add7 is: 9\n", + "the result of the second function is: 9\n", + "the result of the third function is: 10\n" + ] + } + ], + "source": [ + "x = 2\n", + "\n", + "def add7(x):\n", + " result = x + 7\n", + " print(\"the result of add7 is: \", result)\n", + "\n", + "add7(x)\n", + "\n", + "def second_add7():\n", + " x = 2\n", + " result2 = x + 7\n", + " print(\"the result of the second function is: \", result2)\n", + "\n", + "second_add7()\n", + "\n", + "def third_add7(x):\n", + " x=3\n", + " result3 = x + 7\n", + " print(\"the result of the third function is: \", result3)\n", + "\n", + "third_add7(x)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -658,9 +792,9 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "Python [conda env:base] *", "language": "python", - "name": "python3" + "name": "conda-base-py" }, "language_info": { "codemirror_mode": { @@ -672,7 +806,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.13.5" + "version": "3.13.9" } }, "nbformat": 4, diff --git a/02-basic-python/02-bonus-exercises.ipynb b/02-basic-python/02-bonus-exercises.ipynb index e7deb6f..18af707 100644 --- a/02-basic-python/02-bonus-exercises.ipynb +++ b/02-basic-python/02-bonus-exercises.ipynb @@ -27,11 +27,28 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "7.2\n", + "\n" + ] + } + ], "source": [ - "# your code" + "# your code\n", + "a = 3\n", + "b = 4.2\n", + "#type(a)\n", + "#type(b)\n", + "\n", + "c = a + b\n", + "print(c)\n", + "print(type(c))" ] }, { @@ -94,9 +111,9 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "Python [conda env:base] *", "language": "python", - "name": "python3" + "name": "conda-base-py" }, "language_info": { "codemirror_mode": { @@ -108,7 +125,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.13.5" + "version": "3.13.9" } }, "nbformat": 4, diff --git a/03-basic-python-II/lecture-3-basic-python-II.ipynb b/03-basic-python-II/lecture-3-basic-python-II.ipynb index 5e9de5c..25ddee6 100644 --- a/03-basic-python-II/lecture-3-basic-python-II.ipynb +++ b/03-basic-python-II/lecture-3-basic-python-II.ipynb @@ -154,6 +154,7 @@ { "cell_type": "markdown", "metadata": { + "jp-MarkdownHeadingCollapsed": true, "nbpresent": { "id": "a7db497d-427e-40e0-80e0-8f13c131bf79" } @@ -189,122 +190,242 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "nbpresent": { "id": "8e62dd34-888f-432a-987e-573aae66cf6a" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "1 < 2 " ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": { "nbpresent": { "id": "50d05a38-e8e0-4ee0-9905-b461fead8b38" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "1 <= 1" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": { "nbpresent": { "id": "2900a5bb-46f3-4a98-8315-4fae902c2ecf" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "14 == 14" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": { "nbpresent": { "id": "f27ff159-2993-4c0d-a548-5f682dc33acb" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "14 != 14 " ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "# python can also compare strings\n", + "# lexicographical means that it sorts letters and numbers" + ] + }, + { + "cell_type": "code", + "execution_count": 5, "metadata": { "nbpresent": { "id": "16ed88cc-2c1b-4d3c-b15c-61130d31207e" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "\"my text\" == \"my text \"" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": { "nbpresent": { "id": "a679008f-c2cb-47d5-b013-682afb901a71" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "\"my text\" == \"my other text\"" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": { "nbpresent": { "id": "2714c263-fa7f-4d6c-b0b5-20369bd76dfe" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "\"a\" > \"b\"" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, "metadata": { "nbpresent": { "id": "c6ea5872-efcd-4aa0-ae5b-551c4db367af" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "\"a\" < \"b\"" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "\"aa\" < \"aba\"" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "\"aa\" < \"aab\"" ] @@ -344,14 +465,25 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, "metadata": { "nbpresent": { "id": "bfaf1719-3b17-4980-90e1-2e74355dc190" }, "scrolled": true }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "1606938044258990275541962092341162602522202993782792835301376" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "2 ** 200" ] @@ -384,13 +516,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, "metadata": { "nbpresent": { "id": "16141b16-c33c-47f3-a9c0-3f5b6f5e8321" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "(0.1 + 0.1 + 0.1) == 0.3" ] @@ -408,13 +551,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "metadata": { "nbpresent": { "id": "a4d29f2f-f56c-4825-a79d-0ca92f4d6637" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "0.1" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "1 / 10" ] @@ -434,9 +588,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 15, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "a = 0.1 + 0.1 + 0.1 \n", "b = 0.3\n", @@ -456,13 +621,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 16, "metadata": { "nbpresent": { "id": "e357077d-fc73-4415-9c35-3aa66192382e" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# Compare for equality up to a constant value\n", "a < b + 0.00001 and a > b - 0.00001" @@ -483,13 +659,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 17, "metadata": { "nbpresent": { "id": "c9fef2cd-f68c-4793-aa82-244bfd4a999b" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# this is how we import a package\n", "import math \n", @@ -521,23 +708,49 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 21, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hello World\n", + "\n", + "3\n", + "\n" + ] + } + ], "source": [ "# a type annotation for string\n", "greeting: str = \"Hello World\"\n", "print(greeting)\n", + "print(type(greeting))\n", "# we can still override that\n", "greeting = 3\n", - "print(greeting)" + "print(greeting)\n", + "print(type(greeting))" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 25, "metadata": {}, - "outputs": [], + "outputs": [ + { + "ename": "TypeError", + "evalue": "can only concatenate str (not \"int\") to str", + "output_type": "error", + "traceback": [ + "\u001b[31m---------------------------------------------------------------------------\u001b[39m", + "\u001b[31mTypeError\u001b[39m Traceback (most recent call last)", + "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[25]\u001b[39m\u001b[32m, line 5\u001b[39m\n\u001b[32m 2\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mgreet\u001b[39m(name: \u001b[38;5;28mstr\u001b[39m) -> \u001b[38;5;28mstr\u001b[39m:\n\u001b[32m 3\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[33m\"\u001b[39m\u001b[33mHello \u001b[39m\u001b[33m\"\u001b[39m + name\n\u001b[32m----> \u001b[39m\u001b[32m5\u001b[39m greeting = \u001b[43mgreet\u001b[49m\u001b[43m(\u001b[49m\u001b[32;43m3\u001b[39;49m\u001b[43m)\u001b[49m\n\u001b[32m 6\u001b[39m \u001b[38;5;28mprint\u001b[39m(greeting)\n", + "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[25]\u001b[39m\u001b[32m, line 3\u001b[39m, in \u001b[36mgreet\u001b[39m\u001b[34m(name)\u001b[39m\n\u001b[32m 2\u001b[39m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[34mgreet\u001b[39m(name: \u001b[38;5;28mstr\u001b[39m) -> \u001b[38;5;28mstr\u001b[39m:\n\u001b[32m----> \u001b[39m\u001b[32m3\u001b[39m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[33;43m\"\u001b[39;49m\u001b[33;43mHello \u001b[39;49m\u001b[33;43m\"\u001b[39;49m\u001b[43m \u001b[49m\u001b[43m+\u001b[49m\u001b[43m \u001b[49m\u001b[43mname\u001b[49m\n", + "\u001b[31mTypeError\u001b[39m: can only concatenate str (not \"int\") to str" + ] + } + ], "source": [ "# we can also hint at the return type of a function\n", "def greet(name: str) -> str:\n", @@ -585,13 +798,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 26, "metadata": { "nbpresent": { "id": "175038dd-4256-42e4-8e87-fd168e694cf7" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "1.4000000000000004" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "7.4 % 2" ] @@ -609,13 +833,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 27, "metadata": { "nbpresent": { "id": "9fa6132e-6d3e-4bf8-99fb-002a16188e67" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "5" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "x = 2\n", "y = 3\n", @@ -636,13 +871,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 28, "metadata": { "nbpresent": { "id": "68897df7-76f8-4428-83cb-7e915177afdb" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "5" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "x = 2\n", "y = 3\n", @@ -663,13 +909,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 29, "metadata": { "nbpresent": { "id": "6c04cc77-74d3-4fb3-b759-3ab30265b48e" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "-1" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "x = 2\n", "y = 3\n", @@ -679,13 +936,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 30, "metadata": { "nbpresent": { "id": "76beb25a-7f52-489a-b11d-6607484a7177" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "0.6666666666666666" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "x = 2\n", "y = 3\n", @@ -695,13 +963,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 31, "metadata": { "nbpresent": { "id": "9621420b-585f-4e2d-9bf1-0a8215ef0b52" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "32768" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "x = 2\n", "y = 3\n", @@ -732,13 +1011,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 32, "metadata": { "nbpresent": { "id": "4f0a1f6a-a848-4e3e-9877-590c4b4c8d1e" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "10" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "def add(x, y):\n", " result = x + y\n", @@ -760,13 +1050,32 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 33, "metadata": { "nbpresent": { "id": "f2471047-2985-44c0-9233-7d29df07a6e5" } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Within function: only readable in here\n" + ] + }, + { + "ename": "NameError", + "evalue": "name 'function_scope' is not defined", + "output_type": "error", + "traceback": [ + "\u001b[31m---------------------------------------------------------------------------\u001b[39m", + "\u001b[31mNameError\u001b[39m Traceback (most recent call last)", + "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[33]\u001b[39m\u001b[32m, line 12\u001b[39m\n\u001b[32m 7\u001b[39m scope_test()\n\u001b[32m 9\u001b[39m \u001b[38;5;66;03m# If we try to use the function_scope variable outse of the function, we will find that it is not defined. \u001b[39;00m\n\u001b[32m 10\u001b[39m \u001b[38;5;66;03m# This will throw a NameError, because Python doesn't know about that variable here\u001b[39;00m\n\u001b[32m---> \u001b[39m\u001b[32m12\u001b[39m \u001b[38;5;28mprint\u001b[39m(\u001b[33m\"\u001b[39m\u001b[33mOutside function: \u001b[39m\u001b[33m\"\u001b[39m + \u001b[43mfunction_scope\u001b[49m)\n", + "\u001b[31mNameError\u001b[39m: name 'function_scope' is not defined" + ] + } + ], "source": [ "def scope_test():\n", " function_scope = \"only readable in here\"\n", @@ -793,9 +1102,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 34, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a _ _\n", + "_ b _\n", + "AAA _ CC\n", + "_ _ _\n" + ] + } + ], "source": [ "def print_vars(a=\"_\", b=\"_\", c=\"_\"):\n", " print(a, b, c)\n", @@ -818,9 +1138,17 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 35, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('Devin', 'Kutay', 'Shaurya', 'Daniel')\n" + ] + } + ], "source": [ "def var_args(*names):\n", " print(names)\n", @@ -852,13 +1180,25 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 38, "metadata": { "nbpresent": { "id": "8694e33e-6ae9-4f08-9285-95921c365bd2" } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "144 is an even number\n", + "13 is in fact an odd number\n", + "4.2 is an even number\n", + "4.1 is an even number\n", + "0 is an even number\n" + ] + } + ], "source": [ "def isOdd(x):\n", " # the statement within the brackets is evaluated for truth\n", @@ -870,7 +1210,12 @@ " print(str(x), \"is an even number\")\n", "\n", "isOdd(144)\n", - "isOdd(13)" + "isOdd(13)\n", + "\n", + "# other test cases\n", + "isOdd(4.2)\n", + "isOdd(4.1) # things to consider for the homework\n", + "isOdd(0)" ] }, { @@ -898,7 +1243,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 40, "metadata": {}, "outputs": [], "source": [ @@ -928,13 +1273,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 41, "metadata": { "nbpresent": { "id": "84429591-fc62-43ed-af94-ee03f2471b6e" } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0 is false\n", + "An undefined variable is false\n", + "An empty list is false\n", + "An empty string is false\n" + ] + } + ], "source": [ "if 0:\n", " print(\"This should never happen\")\n", @@ -965,13 +1321,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 42, "metadata": { "nbpresent": { "id": "4df31c1d-fa43-4d1b-8d2f-7d5eb7771540" } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2 is a factor of 4\n", + "3 is a factor of 9\n", + "2 is a factor of 12\n", + "Neither 2 nor 3 are factors of 13\n" + ] + } + ], "source": [ "def smallest_factors(x):\n", " # notice the use of the negation and the use of 0 as false\n", @@ -997,13 +1364,25 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 44, "metadata": { "nbpresent": { "id": "4df31c1d-fa43-4d1b-8d2f-7d5eb7771540" } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2 is a factor of 4\n", + "3 is a factor of 9\n", + "2 is a factor of 12\n", + "3 is a factor of 12\n", + "Neither 2 nor 3 are factors of 13\n" + ] + } + ], "source": [ "def factors(x):\n", " # notice the use of the negation and the use of 0 as false\n", @@ -1033,11 +1412,28 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 57, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Hello, Hadley!\n", + "Empty\n" + ] + } + ], "source": [ - "# Try it code goes here" + "# Try it code goes here\n", + "def greeting(name):\n", + " if name != \"\":\n", + " print(\"Hello, \" + name + \"!\")\n", + " else:\n", + " print(\"Empty\")\n", + "\n", + "greeting('Hadley')\n", + "greeting(\"\")" ] }, { @@ -1064,13 +1460,23 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 58, "metadata": { "nbpresent": { "id": "2cccc38c-08c9-47ec-8476-8198b5aef967" } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['0-Paul', '1-John', '2-George', '3-Ringo']\n", + "0-Paul\n", + "1-John\n" + ] + } + ], "source": [ "beatles = [\"0-Paul\", \"1-John\", \"2-George\", \"3-Ringo\"]\n", "# printing the whole array\n", @@ -1090,13 +1496,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 59, "metadata": { "nbpresent": { "id": "2cccc38c-08c9-47ec-8476-8198b5aef967" } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3-Ringo\n", + "2-George\n" + ] + } + ], "source": [ "# access the last element\n", "print(beatles[-1])\n", @@ -1137,9 +1552,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 60, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]" + ] + }, + "execution_count": 60, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "[0] * 10" ] @@ -1200,13 +1626,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 64, "metadata": { "nbpresent": { "id": "6f27c412-dc29-4506-afa2-81e52922d8f2" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "['0-Paul', '1-John']" + ] + }, + "execution_count": 64, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# Get the slice from 0 (included) to 2 (excluded)\n", "beatles[:2] # this can also be written as [0:2]" @@ -1214,9 +1651,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 65, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "['2-George', '3-Ringo']" + ] + }, + "execution_count": 65, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# Sclice from index 2 (3rd element) to end\n", "beatles[2:]" @@ -1224,9 +1672,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 66, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "['0-Paul', '1-John', '2-George', '3-Ringo']" + ] + }, + "execution_count": 66, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# A copy of the list \n", "beatles[:]" @@ -1245,13 +1704,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 67, "metadata": { "nbpresent": { "id": "e47eaccf-7e3a-4c48-a5c8-ead49f46d141" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 67, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "beatles[4:9]" ] @@ -1269,13 +1739,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 68, "metadata": { "nbpresent": { "id": "3797edd3-b4a8-430e-be10-ebc8712b5ef3" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "'Paul'" + ] + }, + "execution_count": 68, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "paul = \"Paul McCartney\"\n", "paul[0:4]" @@ -1296,13 +1777,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 69, "metadata": { "nbpresent": { "id": "7d7aab61-0e11-4084-a70a-537a017c15fa" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "['0-Paul', 'JohnYoko', '2-George', '3-Ringo']" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "beatles[1] = \"JohnYoko\"\n", "beatles" @@ -1317,13 +1809,25 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 70, "metadata": { "nbpresent": { "id": "396b6da4-3fd3-4ef4-b70a-cd22b025e53a" } }, - "outputs": [], + "outputs": [ + { + "ename": "TypeError", + "evalue": "'str' object does not support item assignment", + "output_type": "error", + "traceback": [ + "\u001b[31m---------------------------------------------------------------------------\u001b[39m", + "\u001b[31mTypeError\u001b[39m Traceback (most recent call last)", + "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[70]\u001b[39m\u001b[32m, line 2\u001b[39m\n\u001b[32m 1\u001b[39m \u001b[38;5;66;03m# This will return an error\u001b[39;00m\n\u001b[32m----> \u001b[39m\u001b[32m2\u001b[39m \u001b[43mpaul\u001b[49m\u001b[43m[\u001b[49m\u001b[32;43m1\u001b[39;49m\u001b[43m]\u001b[49m = \u001b[33m\"\u001b[39m\u001b[33mo\u001b[39m\u001b[33m\"\u001b[39m\n", + "\u001b[31mTypeError\u001b[39m: 'str' object does not support item assignment" + ] + } + ], "source": [ "# This will return an error\n", "paul[1] = \"o\"" @@ -1342,13 +1846,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 71, "metadata": { "nbpresent": { "id": "e2a6752b-e74d-48b4-b682-4ea811cef8a4" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "['0-Paul', 'JohnYoko', '2-George', '3-Ringo', '4-George Martin']" + ] + }, + "execution_count": 71, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "beatles.append(\"4-George Martin\")\n", "beatles" @@ -1367,13 +1882,32 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 73, "metadata": { "nbpresent": { "id": "a4109ac9-938f-4db7-b7bb-bb899ad672ed" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "['0-Paul',\n", + " 'JohnYoko',\n", + " '2-George',\n", + " '3-Ringo',\n", + " '4-George Martin',\n", + " 'Jimmy',\n", + " 'Robert',\n", + " 'John',\n", + " 'John']" + ] + }, + "execution_count": 73, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "zeppelin = [\"Jimmy\", \"Robert\", \"John\", \"John\"]\n", "supergroup = beatles + zeppelin\n", @@ -1393,13 +1927,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 74, "metadata": { "nbpresent": { "id": "bc27d3eb-1a47-465d-b1f4-930a833608de" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "4" + ] + }, + "execution_count": 74, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "len(zeppelin)" ] @@ -1417,16 +1962,35 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 79, "metadata": { "nbpresent": { "id": "ab1b9e85-6252-4ee4-aa90-10cb955ab083" } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[['0-Paul', 'JohnYoko', '2-George', '3-Ringo', '4-George Martin'], ['Jimmy', 'Robert', 'John', 'John']]\n" + ] + }, + { + "data": { + "text/plain": [ + "5" + ] + }, + "execution_count": 79, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "bands = [beatles, zeppelin]\n", "bands\n", + "print(bands)\n", "len(bands[0])" ] }, @@ -1443,13 +2007,29 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 77, "metadata": { "nbpresent": { "id": "a37659c5-0da2-4ef0-ba7d-a044ab813be6" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "[['0-Paul', 'JohnYoko', '2-George', '3-Ringo', '4-George Martin'],\n", + " ['Jimmy', 'Robert', 'John', 'John'],\n", + " 1,\n", + " 0.3,\n", + " 17,\n", + " 'This is bad']" + ] + }, + "execution_count": 77, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "bad_bands = bands + [1, 0.3, 17, \"This is bad\"]\n", "# this list contains lists, integers, floats and strings\n", @@ -1469,9 +2049,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 82, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2\n", + "5\n", + "[2 3]\n", + "int64\n" + ] + } + ], "source": [ "import numpy as np\n", "\n", @@ -1493,9 +2084,19 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 83, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['1' 'test' '3' '4' '5']\n", + "\n", + "str672\n" + ] + } + ], "source": [ "# trying to set up a hybrid array; that would be OK in python lists. \n", "my_hybrid_array = np.array([1,\"test\",3,4,5])\n", @@ -1544,13 +2145,21 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 84, "metadata": { "nbpresent": { "id": "b33fcef8-e667-4577-8c01-61a2b4f6ace3" } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, " + ] + } + ], "source": [ "a = 0\n", "\n", @@ -1592,13 +2201,21 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 85, "metadata": { "nbpresent": { "id": "a9a27eaf-b9eb-40e6-ae90-8b5691544af7" } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, " + ] + } + ], "source": [ "a = 1\n", "while True:\n", @@ -1623,20 +2240,28 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 91, "metadata": { "nbpresent": { "id": "e14f20b8-02a7-4a86-b78d-55f2cb27a5e8" } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1, 2, [3], 4, 5, [6], 7, 8, [9], 10, 11, [12], 13, 14, [15], 16, 17, [18], 19, 20, [21], 22, 23, [24], 25, 26, [27], 28, 29, [30], 31, 32, [33], 34, 35, [36], 37, 38, [39], 40, 41, [42], 43, 44, [45], 46, 47, [48], 49, 50, [51], 52, 53, [54], 55, 56, [57], 58, 59, [60], 61, 62, [63], 64, 65, [66], 67, 68, [69], 70, 71, [72], 73, 74, [75], 76, 77, [78], 79, 80, [81], 82, 83, [84], 85, 86, [87], 88, 89, [90], 91, 92, [93], 94, 95, [96], 97, 98, [99], 100, " + ] + } + ], "source": [ "a = 0\n", "while a < 100:\n", " a +=1;\n", " # throw brackets around all numbers divisible by 3\n", " if (not a % 3):\n", - " print(f\"[{a}]\", end=\", \")\n", + " print(f\"[{a}]\", end=\", \") # this is a format string\n", " continue # the next line isn't executed because the flow goes back to the beginning of the loop\n", " print(a, end=\", \")" ] @@ -1652,9 +2277,17 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 92, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "My name is James Holden\n" + ] + } + ], "source": [ "name = \"James Holden\"\n", "print(f\"My name is {name}\")" @@ -1695,13 +2328,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 95, "metadata": { "nbpresent": { "id": "753d2989-7259-4a0d-82cf-648387a730e6" } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Jimmy\n", + "Robert\n", + "John\n", + "John\n" + ] + } + ], "source": [ "for member in zeppelin: \n", " print(member)" @@ -1720,13 +2364,22 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 96, "metadata": { "nbpresent": { "id": "d1cfb14d-a716-40a0-8e7c-5c1e0e0c74d4" } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Jimmy\n", + "Robert\n" + ] + } + ], "source": [ "for member in zeppelin[:2]:\n", " print(member)" @@ -1745,13 +2398,35 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 97, "metadata": { "nbpresent": { "id": "df3c5569-6a10-47f4-a781-e0fd3f43f62f" } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Band Members: \n", + "-------------\n", + "0-Paul\n", + "JohnYoko\n", + "2-George\n", + "3-Ringo\n", + "4-George Martin\n", + "\n", + "Band Members: \n", + "-------------\n", + "Jimmy\n", + "Robert\n", + "John\n", + "John\n", + "\n" + ] + } + ], "source": [ "for band in bands:\n", " print(\"Band Members: \")\n", @@ -1774,9 +2449,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 98, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "range(0, 5)" + ] + }, + "execution_count": 98, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "range(5)" ] @@ -1790,13 +2476,30 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 99, "metadata": { "nbpresent": { "id": "91ec5e27-b2c5-4cf4-959b-5162a3a2e0e9" } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\n", + "1\n", + "2\n", + "3\n", + "4\n", + "5\n", + "6\n", + "7\n", + "8\n", + "9\n" + ] + } + ], "source": [ "for i in range(10): \n", " print (i)" @@ -1811,13 +2514,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 100, "metadata": { "nbpresent": { "id": "439f5d88-4105-42f5-bb30-ad3c0b11f86a" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "[0, 1, 2, 3, 4]" + ] + }, + "execution_count": 100, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "list(range(5))" ] @@ -1831,13 +2545,24 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 101, "metadata": { "nbpresent": { "id": "81fa2227-850e-4d4e-858a-6287c197144a" } }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "[0, 2, 4, 6, 8]" + ] + }, + "execution_count": 101, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# start at 0, stop at index 10, two steps\n", "list(range(0, 10, 2))" @@ -1845,13 +2570,27 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 102, "metadata": { "nbpresent": { "id": "940616b0-2499-49de-bc31-b2b490cf177d" } }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\n", + "-3\n", + "-6\n", + "-9\n", + "-12\n", + "-15\n", + "-18\n" + ] + } + ], "source": [ "for i in range (0, -20, -3):\n", " print(i)" @@ -1868,11 +2607,28 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 110, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "121\n" + ] + } + ], "source": [ - "#Try it! ...code goes here" + "#Try it! ...code goes here\n", + "\n", + "my_sum = 0\n", + "num = 1\n", + "while num <= 21:\n", + " if num % 2 == 1:\n", + " my_sum += num\n", + " num += 1\n", + "\n", + "print(my_sum)" ] }, { @@ -1902,9 +2658,20 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 111, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]" + ] + }, + "execution_count": 111, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# _ is customary for a variable name you won't be using further in the program\n", "[0 for _ in range(10)]" @@ -1912,20 +2679,51 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 112, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "['John',\n", + " 'John',\n", + " 'John',\n", + " 'John',\n", + " 'John',\n", + " 'John',\n", + " 'John',\n", + " 'John',\n", + " 'John',\n", + " 'John']" + ] + }, + "execution_count": 112, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "[\"John\" for _ in range(10)]" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 113, "metadata": { "scrolled": true }, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]" + ] + }, + "execution_count": 113, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "# we can also make use of values we iterate over\n", "[i for i in range(10)]" @@ -1940,9 +2738,29 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 114, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "[0.5137644312215174,\n", + " 0.033538278663964194,\n", + " 0.9668186311896548,\n", + " 0.10554060212019967,\n", + " 0.8220660194770382,\n", + " 0.11197738293296422,\n", + " 0.5960823009473881,\n", + " 0.402286079399646,\n", + " 0.8850967808748391,\n", + " 0.7969925185243779]" + ] + }, + "execution_count": 114, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "import random\n", "rands = [random.random() for _ in range(10)]\n", @@ -1958,9 +2776,29 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 115, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "[5.137644312215174,\n", + " 0.33538278663964194,\n", + " 9.668186311896548,\n", + " 1.0554060212019967,\n", + " 8.220660194770382,\n", + " 1.1197738293296422,\n", + " 5.960823009473881,\n", + " 4.02286079399646,\n", + " 8.850967808748392,\n", + " 7.969925185243779]" + ] + }, + "execution_count": 115, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "[x*10 for x in rands]" ] @@ -1976,10 +2814,23 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 125, "metadata": {}, - "outputs": [], - "source": [] + "outputs": [ + { + "data": { + "text/plain": [ + "[0, 0, 0, 0, 0, 0, 0, 0, 0, 0]" + ] + }, + "execution_count": 125, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "[x%1 for _ in range(10)] #THIS IS WRONG FIX IT PLEASE" + ] }, { "cell_type": "markdown", @@ -2004,9 +2855,27 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 126, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0\n", + "1\n", + "2\n", + "3\n", + "4\n", + "5\n", + "6\n", + "7\n", + "8\n", + "9\n", + "10\n" + ] + } + ], "source": [ "def printNumber(current, limit):\n", " print(current)\n", @@ -2032,9 +2901,27 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 127, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "10\n", + "9\n", + "8\n", + "7\n", + "6\n", + "5\n", + "4\n", + "3\n", + "2\n", + "1\n", + "0\n" + ] + } + ], "source": [ "def printNumberReverse(current, limit):\n", " if current < limit:\n", @@ -2054,9 +2941,38 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], + "execution_count": 128, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Depth before recursive call: 0\n", + "Depth before recursive call: 1\n", + "Depth before recursive call: 2\n", + "Depth before recursive call: 3\n", + "Depth before recursive call: 4\n", + "Depth before recursive call: 5\n", + "Depth before recursive call: 6\n", + "Depth before recursive call: 7\n", + "Depth before recursive call: 8\n", + "Depth before recursive call: 9\n", + "Depth before recursive call: 10\n", + "Returning at depth 10\n", + "Returning at depth 9\n", + "Returning at depth 8\n", + "Returning at depth 7\n", + "Returning at depth 6\n", + "Returning at depth 5\n", + "Returning at depth 4\n", + "Returning at depth 3\n", + "Returning at depth 2\n", + "Returning at depth 1\n", + "Returning at depth 0\n" + ] + } + ], "source": [ "def printCallStack(current, limit):\n", " print(f\"Depth before recursive call: {current}\")\n", @@ -2079,7 +2995,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 129, "metadata": {}, "outputs": [], "source": [ @@ -2091,13 +3007,31 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 130, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/plain": [ + "'0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, '" + ] + }, + "execution_count": 130, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "getNumberString(0, 10)" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, { "cell_type": "code", "execution_count": null, @@ -2109,9 +3043,9 @@ "metadata": { "anaconda-cloud": {}, "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "Python [conda env:base] *", "language": "python", - "name": "python3" + "name": "conda-base-py" }, "language_info": { "codemirror_mode": { @@ -2123,7 +3057,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.13.5" + "version": "3.13.9" }, "nbpresent": { "slides": { diff --git a/04-DescriptiveStatistics.ipynb b/04-DescriptiveStatistics.ipynb new file mode 100644 index 0000000..5010b8b --- /dev/null +++ b/04-DescriptiveStatistics.ipynb @@ -0,0 +1,1925 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "nbpresent": { + "id": "dac6427e-b8df-46f9-bfd3-b24427a73993" + }, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Introduction to Data Science \n", + "# Lecture 4: Introduction to Descriptive Statistics\n", + "*COMP 5360 / MATH 4100, University of Utah, http://datasciencecourse.net/*\n", + "\n", + "In this lecture, we'll cover \n", + "- variable types \n", + "- descriptive statistics in python (min, max, mean, median, std, var, histograms, quantiles) \n", + "- simple plotting functions \n", + "- correlation vs causation\n", + "- confounding variables \n", + "- descriptive vs. inferential statistics\n", + "- discrete and continuous random variables (e.g.: Bernoulli, Binomial, Normal)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Two types of variables\n", + "- **categorical**: records a category (e.g., gender, color, T/F, educational level, Likert scales)\n", + "- **quantitative variables**: records a numerical measurement\n", + "\n", + "Categorical variables might or might not have an order associated with the categories.\n", + "\n", + "In this lecture we'll focus on **quantitative** variables, which can be either **discrete** or **continuous**:\n", + "\n", + "- **discrete variables**: values are discrete (e.g., year born, counts)\n", + "- **continuous variables**: values are real numbers (e.g., length, temperature, time)\n", + "\n", + "(Note categorical variables are always discrete.)\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Quiz!\n", + "\n", + "For each of the following variables, is the variable type categorical, quantitative discrete, or quantitative continuous?\n", + "1. Latitude\n", + "2. Olympic 50 meter race times\n", + "3. Olympic floor gymnastics score\n", + "4. College major\n", + "6. Number of offspring of a rat\n", + "\n", + "\n", + "\n", + "\"https://xkcd.com/435/\"/\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Descriptive statistics (quantitative variables)\n", + "\n", + "The goal is to describe a dataset with a small number of statistics or figures \n", + "\n", + "Suppose we are given a sample, $x_1, x_2, \\ldots, x_n$, of numerical values \n", + "\n", + "Some *descriptive statistics* for quantitative data are the min, max, median, and mean, $\\frac{1}{n} \\sum_{i=1}^n x_i$\n", + "\n", + "\n", + "**Goal**: Use python to compute descriptive statistics. We'll use the python package [numpy](http://www.numpy.org/) for now. " + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "slideshow": { + "slide_type": "slide" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "# First import python packages\n", + "import numpy as np\n", + "import pandas as pd\n", + "\n", + "import matplotlib.pyplot as plt\n", + "#So that graphs are included in the notebook\n", + "%matplotlib inline \n", + "plt.rcParams['figure.figsize'] = (10, 6)\n", + "plt.style.use('ggplot')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Alta monthly average snowfall, October - April\n", + "\n", + "Let's compute descriptive statistics for the monthly average snowfall at Alta. \n", + "\n", + "The snowfall data was collected from 1980 to 2014 and is available at the [Alta Weather and Snow Report webpage](https://www.alta.com/conditions/weather-observations/snowfall-history)." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "nbpresent": { + "id": "61e1167e-99ef-4b5d-b717-07a46077a091" + }, + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "\n", + "\n", + "\n" + ] + } + ], + "source": [ + "Alta_avg_month_snow = [26.60,71.30,90.60,94.40,89.30,96.80,77.10]\n", + "months = ['Oct','Nov','Dec','Jan','Feb','March','Apr']\n", + "\n", + "# Alta_avg_month_snow is a list of floats\n", + "print(type(Alta_avg_month_snow))\n", + "print(type(Alta_avg_month_snow[0]))\n", + "\n", + "# months is a list of strings\n", + "print(type(months))\n", + "print(type(months[0]))" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "7" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# how many months of data do we have?\n", + "len(Alta_avg_month_snow)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "26.6\n", + "96.8\n", + "96.8\n" + ] + } + ], + "source": [ + "# compute the min and max snowfall\n", + "print(np.min(Alta_avg_month_snow))\n", + "print(np.max(Alta_avg_month_snow))\n", + "print(max(Alta_avg_month_snow)) #Can also do this with built-in python function" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "nbpresent": { + "id": "86c3f014-9535-48f0-95a2-df74d16eaa69" + }, + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Index of month with minimal snowfall: 0\n", + "Name of month with minimal snowfall: Oct\n", + "Amount of snowfall in minimal month: 26.6\n", + "\n", + "Index of month with minimal snowfall: 5\n", + "Name of month with minimal snowfall: March\n", + "Amount of snowfall in minimal month: 96.8\n" + ] + } + ], + "source": [ + "# what month do these correspond to? \n", + "imin = np.argmin(Alta_avg_month_snow)\n", + "print('Index of month with minimal snowfall: ', imin)\n", + "print('Name of month with minimal snowfall: ', months[imin])\n", + "print('Amount of snowfall in minimal month: ', Alta_avg_month_snow[imin])\n", + "print()\n", + "\n", + "imax = np.argmax(Alta_avg_month_snow)\n", + "print('Index of month with minimal snowfall: ', imax)\n", + "print('Name of month with minimal snowfall: ', months[imax])\n", + "print('Amount of snowfall in minimal month: ', Alta_avg_month_snow[imax])\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "nbpresent": { + "id": "be5bedf1-b9ed-4caa-bc3e-6c390df97946" + }, + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "78.01428571428572\n" + ] + } + ], + "source": [ + "# compute the mean\n", + "mean_snow = np.mean(Alta_avg_month_snow)\n", + "print(mean_snow)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "nbpresent": { + "id": "4992f285-654f-485e-81ef-8a6ae18cad34" + }, + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "89.3\n" + ] + } + ], + "source": [ + "# compute the median\n", + "median_snow = np.median(Alta_avg_month_snow)\n", + "print(median_snow)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Plotting quantitative data\n", + "\n", + "We can use the python library [matplotlib](https://matplotlib.org/) to make a simple plot of the average monthly snowfall. After all, a picture is worth a thousand words. \n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0 1 2 3 4 5 6]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(np.arange(7), Alta_avg_month_snow) #Note: plot(y) uses x as 0..N-1; plot(x,y) plots x versus y\n", + "print(np.arange(7))\n", + "plt.xticks(np.arange(7),months)\n", + "plt.plot([0,6],[mean_snow,mean_snow], label=\"mean avg. monthly snowfall\")\n", + "plt.plot([0,6],[median_snow,median_snow], label=\"median avg. monthly snowfall\")\n", + "plt.title(\"Alta average monthly snowfall\")\n", + "plt.xlabel(\"month\")\n", + "plt.ylabel(\"snowfall (inches)\")\n", + "plt.legend(loc='lower right')\n", + "#plt.show() #Display all previous plots in one figure\n", + "plt.plot(np.arange(7), Alta_avg_month_snow,'o')\n", + "plt.show() " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nbpresent": { + "id": "de60c848-d1fb-478d-a736-0ebe21762a24" + }, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Population data from the 1994 census\n", + "\n", + "Let's compute some descriptive statistics for age in the 1994 census. We'll use the 'Census Income' dataset available [here](https://archive.ics.uci.edu/ml/datasets/Adult)." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "nbpresent": { + "id": "a6fd92a3-b57e-45c5-b216-f9f475baf8ce" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "# use pandas to import a table of data from a website\n", + "data = pd.read_table(\"http://archive.ics.uci.edu/ml/machine-learning-databases/adult/adult.data\", sep=\",\", \n", + " names=(\"age\", \"type_employer\", \"fnlwgt\", \"education\", \"education_num\", \"marital\", \n", + " \"occupation\", \"relationship\", \"race\",\"sex\",\"capital_gain\", \"capital_loss\", \n", + " \"hr_per_week\",\"country\", \"income\"))\n", + "print(type(data))\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " age type_employer fnlwgt education education_num \\\n", + "0 39 State-gov 77516 Bachelors 13 \n", + "1 50 Self-emp-not-inc 83311 Bachelors 13 \n", + "2 38 Private 215646 HS-grad 9 \n", + "3 53 Private 234721 11th 7 \n", + "4 28 Private 338409 Bachelors 13 \n", + "... ... ... ... ... ... \n", + "32556 27 Private 257302 Assoc-acdm 12 \n", + "32557 40 Private 154374 HS-grad 9 \n", + "32558 58 Private 151910 HS-grad 9 \n", + "32559 22 Private 201490 HS-grad 9 \n", + "32560 52 Self-emp-inc 287927 HS-grad 9 \n", + "\n", + " marital occupation relationship race \\\n", + "0 Never-married Adm-clerical Not-in-family White \n", + "1 Married-civ-spouse Exec-managerial Husband White \n", + "2 Divorced Handlers-cleaners Not-in-family White \n", + "3 Married-civ-spouse Handlers-cleaners Husband Black \n", + "4 Married-civ-spouse Prof-specialty Wife Black \n", + "... ... ... ... ... \n", + "32556 Married-civ-spouse Tech-support Wife White \n", + "32557 Married-civ-spouse Machine-op-inspct Husband White \n", + "32558 Widowed Adm-clerical Unmarried White \n", + "32559 Never-married Adm-clerical Own-child White \n", + "32560 Married-civ-spouse Exec-managerial Wife White \n", + "\n", + " sex capital_gain capital_loss hr_per_week country \\\n", + "0 Male 2174 0 40 United-States \n", + "1 Male 0 0 13 United-States \n", + "2 Male 0 0 40 United-States \n", + "3 Male 0 0 40 United-States \n", + "4 Female 0 0 40 Cuba \n", + "... ... ... ... ... ... \n", + "32556 Female 0 0 38 United-States \n", + "32557 Male 0 0 40 United-States \n", + "32558 Female 0 0 40 United-States \n", + "32559 Male 0 0 20 United-States \n", + "32560 Female 15024 0 40 United-States \n", + "\n", + " income \n", + "0 <=50K \n", + "1 <=50K \n", + "2 <=50K \n", + "3 <=50K \n", + "4 <=50K \n", + "... ... \n", + "32556 <=50K \n", + "32557 >50K \n", + "32558 <=50K \n", + "32559 <=50K \n", + "32560 >50K \n", + "\n", + "[32561 rows x 15 columns]\n" + ] + } + ], + "source": [ + "print(data)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[39, 50, 38, 53, 28, 37, 49, 52, 31, 42, 37, 30, 23, 32, 40, 34, 25, 32, 38, 43, 40, 54, 35, 43, 59, 56, 19, 54, 39, 49, 23, 20, 45, 30, 22, 48, 21, 19, 31, 48, 31, 53, 24, 49, 25, 57, 53, 44, 41, 29, 25, 18, 47, 50, 47, 43, 46, 35, 41, 30, 30, 32, 48, 42, 29, 36, 28, 53, 49, 25, 19, 31, 29, 23, 79, 27, 40, 67, 18, 31, 18, 52, 46, 59, 44, 53, 49, 33, 30, 43, 57, 37, 28, 30, 34, 29, 48, 37, 48, 32, 76, 44, 47, 20, 29, 32, 17, 30, 31, 42, 24, 38, 56, 28, 36, 53, 56, 49, 55, 22, 21, 40, 30, 29, 19, 47, 20, 31, 35, 39, 28, 24, 38, 37, 46, 38, 43, 27, 20, 49, 61, 27, 19, 45, 70, 31, 22, 36, 64, 43, 47, 34, 33, 21, 52, 48, 23, 71, 29, 42, 68, 25, 44, 28, 45, 36, 39, 46, 18, 66, 27, 28, 51, 27, 28, 27, 21, 34, 18, 33, 44, 43, 30, 40, 37, 34, 41, 53, 31, 58, 38, 24, 41, 47, 41, 23, 36, 40, 35, 24, 26, 19, 51, 42, 37, 18, 36, 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33, 53, 35, 31, 18, 45, 28, 22, 55, 45, 22, 37, 28, 19, 37, 50, 31, 40, 51, 56, 21, 40, 22, 47, 44, 30, 44, 41, 47, 26, 34, 47, 36, 21, 45, 33, 33, 58, 31, 32, 44, 24, 35, 43, 49, 37, 42, 31, 19, 41, 51, 51, 63, 39, 30, 62, 27, 32, 37, 47, 31, 42, 37, 60, 42, 38, 24, 34, 20, 29, 90, 55, 36, 49, 50, 17, 54, 26, 44, 28, 54, 21, 24, 31, 59, 41, 29, 50, 32, 42, 47, 44, 49, 61, 65, 45, 59, 30, 34, 24, 42, 37, 36, 21, 54, 34, 41, 18, 26, 23, 63, 34, 54, 37, 54, 22, 32, 42, 31, 48, 28, 31, 28, 24, 50, 26, 37, 24, 18, 32, 23, 33, 49, 75, 74, 26, 66, 34, 18, 33, 36, 44, 36, 53, 60, 28, 36, 35, 45, 23, 35, 34, 46, 58, 55, 63, 41, 45, 41, 42, 90, 41, 22, 53, 49, 51, 22, 23, 59, 40, 28, 39, 25, 48, 62, 44, 28, 62, 32, 59, 20, 40, 47, 60, 55, 18, 43, 31, 22, 56, 41, 24, 42, 53, 52, 42, 48, 35, 33, 20, 33, 30, 31, 29, 26, 61, 45, 29, 57, 33, 20, 26, 36, 23, 31, 47, 61, 35, 23, 20, 41, 39, 51, 61, 51, 36, 41, 34, 25, 37, 19, 66, 23, 30, 53, 25, 18, 51, 61, 53, 17, 61, 44, 38, 40, 32, 46, 50, 36, 30, 33, 36, 85, 62, 24, 48, 58, 45, 66, 37, 55, 39, 58, 50, 28, 34, 41, 36, 22, 35, 49, 21, 64, 41, 52, 32, 27, 48, 28, 24, 51, 32, 61, 60, 33, 42, 24, 82, 26, 18, 34, 57, 25, 34, 71, 35, 47, 50, 33, 38, 50, 45, 32, 39, 25, 20, 46, 40, 66, 30, 36, 57, 46, 27, 33, 58, 30, 26, 81, 32, 22, 31, 29, 35, 30, 34, 54, 37, 22, 34, 30, 38, 71, 45, 41, 72, 45, 31, 39, 37, 43, 65, 43, 43, 32, 43, 32, 53, 22, 27, 40, 58, 22, 52]\n" + ] + } + ], + "source": [ + "# export a list containing ages of people in 1994 Census\n", + "ages = data[\"age\"].tolist()\n", + "print(ages)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "nbpresent": { + "id": "b79fa570-8c08-4820-a035-2a00bfae1a9b" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "32561\n", + "17\n", + "90\n", + "38.58164675532078\n", + "37.0\n" + ] + } + ], + "source": [ + "# now use numpy to compute descriptive statistics for ages\n", + "print(len(ages))\n", + "print(np.min(ages))\n", + "print(np.max(ages))\n", + "print(np.mean(ages))\n", + "print(np.median(ages))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nbpresent": { + "id": "674ee724-0165-40c5-9296-83db8305fa4c" + }, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Histograms\n", + "\n", + "We can also make a histogram using the python library [matplotlib](https://matplotlib.org/) to show the distribution of ages in the dataset. " + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "nbpresent": { + "id": "06d04c6d-90a4-441d-9d6e-4f719490e12e" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(ages,np.arange(0,100,4)) # Use bins defined by np.arange(0,100,4) # numbers from 0 to 100 in intervals of 4\n", + "#plt.hist(ages) # Use 10 bins\n", + "plt.title(\"1994 Census Histogram\")\n", + "plt.xlabel(\"Age\")\n", + "plt.ylabel(\"Frequency\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nbpresent": { + "id": "e6a51e7a-d63e-4187-8899-bfbf03f8a4b6" + }, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Quantiles \n", + "For a fixed percent $p$, the corresponding quantile (also called percentile) is the value such that $p$ percent of the observations in the sample are smaller than that value. " + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "nbpresent": { + "id": "a912604c-786a-448e-a908-397f28b46a13" + }, + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "28.0\n", + "48.0\n" + ] + } + ], + "source": [ + "print(np.percentile(ages,25))\n", + "print(np.percentile(ages,75))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "For this data, 25% of the people are under 28 years old\n", + "\n", + "The middle 50% of the data (the data between the 25% and 75% quantiles) is between 28 and 48 years old \n", + "\n", + "**Question**: how do I read off quantiles from a histogram? " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Variance and Standard Deviation\n", + "\n", + "Variance and standard deviation quantify the amount of variation or dispersion of a set of data values.\n", + "\n", + "Mean, $\\mu = \\frac{1}{n} \\sum_{i = 1}^n x_i$
\n", + "Variance $= \\sigma^2 = \\frac{1}{n-1} \\sum_{i = 1}^n (x_i - \\mu)^2$
\n", + "Std. dev. $= \\sigma$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "186.05568600783081\n", + "13.640223092304275\n" + ] + } + ], + "source": [ + "print(np.var(ages))\n", + "print(np.std(ages))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "In terms of the histogram,...\n", + "\"https://en.wikipedia.org/wiki/Correlation_and_dependence#/media/File:Correlation_examples2.svg\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Covariance and Correlation\n", + "Covariance and correlation measure of how much two variables change together.\n", + "\n", + "The *covariance* of two variables $x$ and $y$ is given by\n", + "$$\n", + "cov(x,y) = \\frac{1}{n-1} \\sum_{i=1}^n (x_i - \\mu_x)(y_i - \\mu_y),\n", + "$$ \n", + "where\n", + "+ $\\mu_x$ is mean of $x_1,x_2,\\ldots,x_n$ and\n", + "+ $\\mu_y$ is mean of $y_1,y_2,\\ldots,y_n$.\n", + "\n", + "The *correlation coefficient* of two variables $x$ and $y$ is given by \n", + "$$\n", + "corr(x,y) = \\frac{cov(x,y)}{\\sigma_x \\sigma_y},\n", + "$$\n", + "where\n", + "+ $\\sigma_x$ is std. dev. of $x_1,x_2,\\ldots,x_n$ and \n", + "+ $\\sigma_y$ is std. dev. of $y_1,y_2,\\ldots,y_n$.\n", + "\n", + "Recall that always $-1 \\leq corr(x,y) \\leq 1$.\n", + "\n", + "

\n", + "Here is a plot of several pairs of variables, together with the correlation coefficient:\n", + "\"https://en.wikipedia.org/wiki/Correlation_and_dependence#/media/File:Correlation_examples2.svg\"\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "In 1994 consensus data, let's use numpy to find the correlation between age and hr_per_week" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "hr = data[\"hr_per_week\"].tolist()\n", + "\n", + "plt.hist2d(ages,hr,bins=25)\n", + "plt.title(\"Age vs. Hours worked per week\")\n", + "plt.xlabel(\"Age\")\n", + "plt.ylabel(\"Hours worked per week\")\n", + "plt.show()\n", + "plt.plot(ages,hr,'o')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1. , 0.06875571],\n", + " [0.06875571, 1. ]])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.corrcoef(ages,hr)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Correlation vs Causation\n", + "\n", + "\"https://xkcd.com/552/\"\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Spurious Correlations I (www.tylervigen.com)\n", + "\n", + "\"www.tylervigen.com\"\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Spurious Correlations II (www.tylervigen.com)\n", + "\n", + "\"www.tylervigen.com\"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Confounding: example\n", + "\n", + "Suppose we are given city statistics covering a four-month summer period. \n", + "We observe that swimming pool deaths tend to increase on days when more ice cream is sold. \n", + "\n", + "Should we conclude that ice cream is the killer? " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Confounding: example cont.\n", + "\n", + "No! \n", + "\n", + "As astute analysts, we identify average daily temperature as a confounding variable: on hotter days, people are more likely to both buy ice cream and visit swimming pools. \n", + "\n", + "Regression methods can be used to statistically control for this confounding variable, eliminating the direct relationship between ice cream sales and swimming pool deaths.\n", + "\n", + "

\n", + "\n", + "\n", + "**source**: Jacob Westfall and Tal Yarkoni, Statistically Controlling for Confounding Constructs Is Harder than You Think, PLOS One (2016). [link](https://doi.org/10.1371/journal.pone.0152719) \n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## In Class Activity\n", + "\n", + "Open jupyter notebook 04-DescriptiveStatistics_Activity.ipynb." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Descriptive vs. Inferential Statistics \n", + "\n", + "Descriptive statistics quantitatively describe or summarize features of a dataset. \n", + "\n", + "Inferential statistics attempts to learn about the population from which the data was sampled. \n", + "\n", + "**Example**: The week before a US presidential election, it is not possible to ask every voting person who they intend to vote for. Instead, a relatively small number of individuals are surveyed. The *hope* is that we can determine the population's preferred candidate from the surveyed results. \n", + "\n", + "Often, we will model a population characteristic as a *probability distribution*. \n", + "\n", + "*Inferential statistics* is deducing properties of an underlying probability distribution from sampled data. \n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Bernoulli Distribution\n", + "\n", + "The Bernoulli distribution, named after Jacob Bernoulli, is the probability distribution of a random variable which takes the value 1 (success) with probability $p$ and the value 0 (failure) with probability $q=1-p$. \n", + "\n", + "The Bernoulli distribution with $p=0.5$ (implying $q=0.5$) describes a 'fair' coin toss where 1 and 0 represent \"heads\" and \"tails\", respectively. If the coin is unfair, then we would have that $p\\neq 0.5$.\n", + "\n", + "We can use python to sample from the Bernoulli probability distribution. " + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "slideshow": { + "slide_type": "slide" + }, + "tags": [] + }, + "outputs": [], + "source": [ + "import scipy as sc\n", + "from scipy.stats import bernoulli, binom, norm" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1 0 0 1 0 1 0 1 1 0 0 1 0 0 0 0 1 1 0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 1 1 0 0\n", + " 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 0 1 1 1 1 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1\n", + " 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 1 0 1 1 0 1 0 1 1 1 1 0\n", + " 1 0 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0\n", + " 1 1 1 1 1 0 0 1 0 1 0 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 1\n", + " 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 1 0 1 1 0 0 1 0 1 1 0 0 0 1\n", + " 0 1 1 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1\n", + " 1 1 0 0 0 1 1 0 0 1 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 1 0 1 0 0 1 1 0 1 0 1 0\n", + " 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 1 1 0 1 0 0 1 0 0 1\n", + " 0 0 1 1 1 1 1 0 1 0 1 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 0 0 0 1 0 0\n", + " 1 1 1 1 1 1 0 1 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 1 0 1 1 0 0 1 1 0\n", + " 0 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 0 0 1 1 1 0 1 1 1 1 1 1 0 0 1 0 1 1\n", + " 1 1 1 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 1 1\n", + " 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 1 1 0 0 1 0 1 0 1 1 0 1\n", + " 0 0 1 0 0 0 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0\n", + " 0 0 1 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 0\n", + " 0 1 0 0 0 1 1 0 1 1 1 0 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 1 0 1 0\n", + " 0 0 0 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 0 1 1 0\n", + " 1 1 1 1 1 0 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 1 1 1 1 0\n", + " 0 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 1 1 1 1 0 1 0 0 0 0 1 1 1 0 1 0 0 0 1 1 0\n", + " 0 1 0 1 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1\n", + " 0 0 1 1 1 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 0 1 0 0\n", + " 1 1 0 0 0 1 0 1 0 1 1 1 1 0 0 0 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 1 0 1 1 0\n", + " 1 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0 0 0\n", + " 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 0 1 1 0 0\n", + " 0 1 0 0 0 0 1 1 1 1 0 1 0 0 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 1\n", + " 1 0 1 0 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0\n", + " 0]\n" + ] + } + ], + "source": [ + "n = 1000;\n", + "coin_flips = bernoulli.rvs(p=0.5, size=n)\n", + "print(coin_flips)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "How many heads did we get? We just count the number of 1's. " + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "506\n", + "0.506\n" + ] + } + ], + "source": [ + "print(sum(coin_flips))\n", + "print(sum(coin_flips)/n)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "What if we flip the coin more times? " + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.499803\n" + ] + } + ], + "source": [ + "n = 1000000\n", + "coin_flips = bernoulli.rvs(p=0.5, size=n)\n", + "print(sum(coin_flips)/n)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "Some facts about Bernoulli variables: \n", + "* mean is p\n", + "* variance is p(1-p)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Binomial distribution\n", + "\n", + "The binomial distribution, with parameters $n$ and $p$, is a discrete probability distribution describing the total number of \"successes\" in $n$ Bernoulli random variables. For simplicity, take $p=0.5$ so that the Bernoulli distribution describes the outcome of a coin. For each flip, the probability of heads is $p$ (so the probability of tails is $q=1-p$). But we don't keep track of the individual flips. We only keep track of how many heads/tails there were in total. So, the binomial distribution can be thought of as summarizing a bunch of (independent) Bernoulli random variables. \n", + "\n", + "The following code is equivalent to flipping a fair (p=0.5) coin n=10 times and counting the number of heads and then repeating this process 1,000,000 times. " + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "scrolled": true, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 2 4 5 5 4 5 6 7 5 6 5 3 7 4 7 6 5 3 8 4 5 6 5 4\n", + " 4 6 5 8 5 4 4 6 3 3 5 8 4 10 5 3 5 5 7 3 5 5 4 7\n", + " 7 6 7 7 5 4 3 5 5 5 8 4 6 7 2 5 5 4 3 6 8 7 5 5\n", + " 3 2 4 5 5 5 3 4 7 6 4 3 4 4 7 6 4 6 1 6 1 3 7 6\n", + " 3 4 5 4]\n" + ] + } + ], + "source": [ + "p = 0.5\n", + "n = 10\n", + "bin_vars = binom.rvs(n=n,p=p,size=1000000)\n", + "print(bin_vars[:100])" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "scrolled": true, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-0.5 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "bins=np.arange(12)-.5\n", + "print(bins)\n", + "plt.figure(figsize=(6, 3))\n", + "plt.hist(bin_vars, bins=bins,density=True)\n", + "plt.title(\"A histogram of binomial random variables\")\n", + "plt.xlim([-.5,10.5])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "Some facts about the binomial distribution: \n", + "* The mean is $np$\n", + "* The variance is $np(1-p)$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Discrete random variables and probability mass functions \n", + "\n", + "The Binomial and Bernoulli random variables are examples of *discrete random variables* since they can take only discrete values. A Bernoulli random variable can take values $0$ or $1$. A binomial random variable can only take values \n", + "$$\n", + "0,1,\\ldots, n. \n", + "$$\n", + "One can compute the probability that the variable takes each value. This is called the *probability mass function*. \n", + "For a Bernoulli random variable, the probability mass function is given by \n", + "$$\n", + "f(k) = \\begin{cases} p & k=1 \\\\ 1-p & k = 0 \\end{cases}\n", + "$$\n", + "For a binomial random variable, the probability mass function is given by \n", + "$$\n", + "f(k) = \\binom{n}{k} p^k (1-p)^{n-k}.\n", + "$$\n", + "Here, $\\binom{n}{k} = \\frac{n!}{k!(n-k)!}$ is the number of ways to arrange the\n", + "$k$ heads among the $n$ flips. For a fair coin, we have $p=0.5$ and $f(k) = \\binom{n}{k} \\frac{1}{2^n}$. This is the number of ways to arrange $k$ heads among $n$ outcomes divided by the total number of outcomes. \n", + "\n", + "The probability mass function can be plotted using the scipy library as follows." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "f = lambda k: binom.pmf(k, n=n,p=p)\n", + "\n", + "x = np.arange(n+1);\n", + "plt.plot(x, f(x),'*-')\n", + "plt.title(\"Probability mass function for a Binomial random variable\")\n", + "plt.xlim([0,n])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "Observe that the probability mass function looks very much like the histogram plot! (not a coincidence) \n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Concept check\n", + "\n", + "**Question**: what is a discrete random variable? \n", + "\n", + "A *discrete random variable (r.v.)* is an abstraction of a coin. It can take on a *discrete* set of possible different values, each with a preassigned probability. We saw two examples of discrete random variables: Bernoulli and binomial. A Bernoulli r.v. takes value $1$ with probability $p$ and $0$ with probability $1-p$. A binomial r.v. takes values $0,1,\\ldots,n$, with a given probability. The probabilities are given by the probability mass function. This function looks just like the histogram for a sample of a large number of random variables. \n", + "\n", + "You can use the same descriptive statistics to describe a discrete random value (min, max, mean, variance, etc..).\n", + "\n", + "**Question**: what is the random variable that describes a fair dice? the sum of two fair dice? " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Normal (Gaussian) distribution \n", + "\n", + "Roughly speaking, normal random variables are described by a \"bell curve\". The curve is centered at the mean, $\\mu$, and has width given by the standard deviation, $\\sigma$. " + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "mu = 0 # mean\n", + "sigma = 1 # standard deviation \n", + "x = np.arange(mu-4*sigma,mu+4*sigma,0.001);\n", + "pdf = norm.pdf(x,loc=mu, scale=sigma)\n", + "# Here, I could have also written\n", + "# pdf = 1/(sigma * sc.sqrt(2 * sc.pi)) * sc.exp( - (x - mu)**2 / (2 * sigma**2)) \n", + "plt.plot(x, pdf, linewidth=2, color='k')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Continuous random variables and probability density functions \n", + "\n", + "A normal random variable is an example of a *continuous* random variable. A normal random variable can take any real value, but some numbers are more likely than others. More formally, we say that the *probability density function (PDF)* for the normal (Gaussian) distribution is\n", + "$$\n", + "f(x) = \\frac{1}{\\sqrt{ 2 \\pi \\sigma^2 }}\n", + "e^{ - \\frac{ (x - \\mu)^2 } {2 \\sigma^2} },\n", + "$$\n", + "where $\\mu$ is the mean and $\\sigma$ is the variance. What this means is that the probability that a normal random variable will take values in the interval $[a,b]$ is given by \n", + "$$\n", + "\\int_a^b f(x) dx.\n", + "$$\n", + "This is just the area under the curve for this interval. For $a=\\mu-\\sigma$ and $b = \\mu+\\sigma$, we plot this below." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(x, pdf, linewidth=2, color='k')\n", + "x2 = np.arange(mu-sigma,mu+sigma,0.001)\n", + "plt.fill_between(x2, y1= norm.pdf(x2,loc=mu, scale=sigma), facecolor='red', alpha=0.5)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "One can check that \n", + "$$\n", + "\\int_{-\\infty}^\\infty f(x)\\, dx = 1\n", + "$$\n", + "which just means that the probability that the random variable takes value between $-\\infty$ and $\\infty$ is one. \n", + "\n", + "This integral can be computed using the *cumulative distribution function* (CDF)\n", + "$$\n", + "F(x) = \\int_{-\\infty}^x f(t)\\, dt = \\text{Prob. random variable }\\leq x .\n", + "$$\n", + "We have that \n", + "$$\n", + "\\int_a^b f(x)\\, dx = F(b) - F(a)\n", + "$$\n" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "text/plain": [ + "np.float64(0.6826894921370859)" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "norm.cdf(mu+sigma, loc=mu, scale=sigma) - norm.cdf(mu-sigma, loc=mu, scale=sigma) " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "This means that 68% of the time, this normal random variable will have values between $\\mu-\\sigma$ and $\\mu+\\sigma$. \n", + "\n", + "You used to have to look these values up in a table! \n", + "\n", + "Let's see what it looks like if we sample 1,000,000 normal random variables and then plot a histogram. " + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "slideshow": { + "slide_type": "-" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0.22205339 -0.35805089 -0.4761207 -0.09553349 -0.03255357 0.09416537\n", + " -0.41561191 0.12244982 -0.13841279 0.89045474 -0.18220864 0.09522675\n", + " -0.46475558 -0.89468059 0.32340686 -0.24042333 0.14852674 0.51306118\n", + " 1.22341052 -0.12798745 0.39610647 -0.08346062 0.05975998 -0.91910696\n", + " -1.16309764 2.27402516 -0.52524946 -0.58306812 -0.71772582 -0.64498557\n", + " -0.18412571 -0.990271 -0.88549884 1.69982646 -0.0153694 -1.32163653\n", + " -0.33667973 -0.43220282 -0.36078704 0.82876988 0.30465869 0.35882095\n", + " -1.03171267 0.73244056 -0.79204441 -0.35452768 0.31417668 -0.6723341\n", + " 0.57060451 1.42587616 -1.00930922 -0.11296348 0.32394417 -0.40211796\n", + " 0.83001976 -0.32390293 -0.99126272 -1.26521123 -0.50855882 -1.22309632\n", + " -0.76223431 -1.98417714 -0.51767666 1.24798155 -0.12988421 0.21660857\n", + " 2.13760285 -0.73806226 -2.03545658 -0.90034255 -0.49575031 0.14701301\n", + " -0.88489896 0.15432633 1.22316056 0.09782962 1.11877398 -1.05263047\n", + " 0.10792072 -0.71695637 1.14855718 0.23040684 0.35712321 -0.50219559\n", + " 0.53770549 -0.06896089 1.89759589 -0.80484557 -1.20195909 1.42036192\n", + " -3.96938149 1.4696986 -0.95857068 -0.1231198 -0.44416647 0.17411569\n", + " 1.77995792 -0.23913301 0.34141569 2.14899329]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "norm_vars = norm.rvs(loc=mu,scale=sigma,size=1000000)\n", + "print(norm_vars[:100])\n", + "\n", + "plt.hist(norm_vars, bins=100,density=True)\n", + "plt.plot(x, pdf, linewidth=2, color='k')\n", + "plt.title(\"A histogram of normal random variables\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "When $n$ is large, the histogram of the sampled variables looks just like the probability distribution function!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Time permitting: explore categorical variables\n", + "\n", + "Note: the descriptive statistics and discussed in this lecture can only be computed for quantitative variables. Similarly, histograms, pdf's, and cdf's only apply to quantitative variables\n", + "\n", + "Recall the data frame we previsouly made from the 1994 census data:\n" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "marital\n", + "Married-civ-spouse 14976\n", + "Never-married 10683\n", + "Divorced 4443\n", + "Separated 1025\n", + "Widowed 993\n", + "Married-spouse-absent 418\n", + "Married-AF-spouse 23\n", + "Name: count, dtype: int64 \n", + "\n", + "marital\n", + "Married-civ-spouse 0.459937\n", + "Never-married 0.328092\n", + "Divorced 0.136452\n", + "Separated 0.031479\n", + "Widowed 0.030497\n", + "Married-spouse-absent 0.012837\n", + "Married-AF-spouse 0.000706\n", + "Name: proportion, dtype: float64 \n", + "\n", + "sex\n", + "Male 0.669205\n", + "Female 0.330795\n", + "Name: proportion, dtype: float64 \n", + "\n", + "income\n", + "<=50K 0.75919\n", + ">50K 0.24081\n", + "Name: proportion, dtype: float64 \n", + "\n" + ] + }, + { + "data": { + "text/plain": [ + "sex income\n", + "Female <=50K 0.890539\n", + " >50K 0.109461\n", + "Male <=50K 0.694263\n", + " >50K 0.305737\n", + "Name: proportion, dtype: float64" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#print(data)\n", + "print(data[\"marital\"].value_counts(),\"\\n\")\n", + "print(data[\"marital\"].value_counts(normalize=True),\"\\n\")\n", + "print(data[\"sex\"].value_counts(normalize=True),\"\\n\")\n", + "print(data[\"income\"].value_counts(normalize=True),\"\\n\")\n", + "data.groupby(['sex'])['income'].value_counts(normalize=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "nbpresent": { + "id": "558af430-f4c0-4be9-b1ef-afce5fccd0fa" + }, + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Concept recap\n", + "- variable types \n", + "- descriptive statistics in python (min, max, mean, median, std, var, histograms, quantiles) \n", + "- correlation vs causation\n", + "- confounding variables \n", + "- descriptive vs. inferential statistics\n", + "- discrete and continuous random variables (e.g.: Bernouilli, Binomial, Normal)\n", + "\n", + "\n", + "## Looking ahead: Hypothesis testing" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "celltoolbar": "Slideshow", + "kernelspec": { + "display_name": "Python [conda env:base] *", + "language": "python", + "name": "conda-base-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.9" + }, + "nbpresent": { + "slides": { + "006f01ca-e160-4faa-ad02-2f873362ca99": { + "id": "006f01ca-e160-4faa-ad02-2f873362ca99", + "prev": "e60ea09b-1474-49b0-9ea6-2e803b335693", + "regions": { + "88222835-28de-4a0f-895e-303024baf060": { + "attrs": { + 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"\n", + "\n", + "Your Name: \n", + "Your UID: \n", + "Your E-Mail: \n", + "\n", + "For this activity first import a small data set containing 10 measurements of CO$_2$ levels and global temperatures. You can do this with the read_csv command from the pandas library as follows: " + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "my_data = pd.read_csv(\"co2_and_temp_data.csv\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Item 1\n", + "\n", + "Print the first few rows of the my_data data frame. Then create lists storing the CO_2 and temperature values. Compute the mean and median of the temperature measurements." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " CO_2 Temp\n", + "0 314 13.9\n", + "1 317 14.0\n", + "2 320 13.9\n", + "3 326 14.1\n", + "4 331 14.0\n", + "5 339 14.3\n", + "6 346 14.1\n", + "7 354 14.5\n", + "8 361 14.5\n", + "9 369 14.4\n" + ] + } + ], + "source": [ + "# Your code \n", + "print(my_data)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Item 2\n", + "\n", + "Make a scatterplot of CO_2 versus temperature. What is the correlation cofficient between these two variables? " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1. , 0.89197636],\n", + " [0.89197636, 1. ]])" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Your code here\n", + "plt.plot(my_data[\"CO_2\"], my_data[\"Temp\"],'o')\n", + "plt.show\n", + "np.corrcoef(my_data[\"CO_2\"],my_data[\"Temp\"])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "*Your answers here.*" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Item 3\n", + "\n", + "Change the last temperature measurement from 14.4 degrees to 144 degrees which could have happened if there was a small error in manual data entry. \n", + "\n", + "How are the mean and median affected?\n", + "\n", + "How are the scatterplot and the correlation coefficient affected?\n", + "\n", + "Are the mean, median, and correlation coefficient robust to outliers and data entry errors?" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "# Your code here" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "*Your answers here.*" + ] + } + ], + "metadata": { + "anaconda-cloud": {}, + "celltoolbar": "Slideshow", + "kernelspec": { + "display_name": "Python [conda env:base] *", + "language": "python", + "name": "conda-base-py" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.9" + }, + "nbpresent": { + "slides": { + "006f01ca-e160-4faa-ad02-2f873362ca99": { + "id": "006f01ca-e160-4faa-ad02-2f873362ca99", + "prev": "e60ea09b-1474-49b0-9ea6-2e803b335693", + "regions": { + "88222835-28de-4a0f-895e-303024baf060": { + "attrs": { + "height": 0.8, + "width": 0.8, + "x": 0.1, + "y": 0.1 + }, + "content": { + "cell": "e6a51e7a-d63e-4187-8899-bfbf03f8a4b6", + "part": "whole" + }, + "id": "88222835-28de-4a0f-895e-303024baf060" + } + } + }, + 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