Learn-Coding/Statistics.html at main · mithleshprasad/Learn-Coding · GitHub

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<!DOCTYPE html>
<html lang="en">
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    <title>Statistics Formulas</title>
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    <h1>Statistics Formulas</h1>
    <div class="container">
        <!-- Measures of Central Tendency -->
        <section>
            <h2>Measures of Central Tendency</h2>
            <div class="formula">Mean (μ) = \\( \frac{\sum_{i=1}^{n} x_i}{n} \\)</div>
            <div class="formula">Median: The middle value of a dataset (for an ordered set)</div>
            <div class="formula">Mode: The most frequent value in a dataset</div>
        </section>

        <!-- Measures of Dispersion -->
        <section>
            <h2>Measures of Dispersion</h2>
            <div class="formula">Variance (σ²) = \\( \frac{\sum_{i=1}^{n} (x_i - \mu)^2}{n} \\)</div>
            <div class="formula">Standard Deviation (σ) = \\( \sqrt{\text{Variance}} \\)</div>
            <div class="formula">Range = \\( \text{Max} - \text{Min} \\)</div>
        </section>

        <!-- Probability -->
        <section>
            <h2>Probability</h2>
            <div class="formula">Probability of an event: \\( P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \\)</div>
            <div class="formula">Complement Rule: \\( P(E') = 1 - P(E) \\)</div>
            <div class="formula">Addition Rule: \\( P(A \cup B) = P(A) + P(B) - P(A \cap B) \\)</div>
            <div class="formula">Multiplication Rule: \\( P(A \cap B) = P(A) \cdot P(B|A) \\)</div>
        </section>

        <!-- Probability Distributions -->
        <section>
            <h2>Probability Distributions</h2>
            <div class="formula">Binomial Distribution: \\( P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k} \\)</div>
            <div class="formula">Normal Distribution: \\( P(X) = \frac{1}{\sigma \sqrt{2 \pi}} \cdot e^{-\frac{(X - \mu)^2}{2 \sigma^2}} \\)</div>
        </section>

        <!-- Hypothesis Testing -->
        <section>
            <h2>Hypothesis Testing</h2>
            <div class="formula">Null Hypothesis (H₀): The hypothesis stating no effect or no difference.</div>
            <div class="formula">Alternative Hypothesis (H₁): The hypothesis stating there is an effect or difference.</div>
            <div class="formula">Test Statistic (z): \\( z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}} \\)</div>
            <div class="formula">p-value: The probability of observing a result at least as extreme as the result obtained, under the null hypothesis.</div>
        </section>

        <!-- Correlation and Regression -->
        <section>
            <h2>Correlation and Regression</h2>
            <div class="formula">Pearson's Correlation Coefficient: \\( r = \frac{n \sum xy - \sum x \sum y}{\sqrt{(n \sum x^2 - (\sum x)^2)(n \sum y^2 - (\sum y)^2)}} \\)</div>
            <div class="formula">Simple Linear Regression Equation: \\( Y = a + bX \\), where a = intercept, b = slope</div>
        </section>

        <!-- Confidence Interval -->
        <section>
            <h2>Confidence Interval</h2>
            <div class="formula">Confidence Interval: \\( \mu \pm Z \cdot \frac{\sigma}{\sqrt{n}} \\)</div>
            <div class="formula">where Z is the Z-score corresponding to the confidence level.</div>
        </section>
    </div>
    <footer>
        &copy; 2024 Statistics Guide. All Rights Reserved.
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