diff --git a/public/data/wellbeing-population.csv b/public/data/wellbeing-population.csv
index b887b99..f206bdd 100644
--- a/public/data/wellbeing-population.csv
+++ b/public/data/wellbeing-population.csv
@@ -55,7 +55,7 @@ id,programme,stress,sleep_hours,exam_score
54,Psychology,5.85,4.13,58.9
55,Business,0.73,7.32,84.4
56,Psychology,13.68,7.46,57.2
-57,Psychology,40.00,6.53,54.4
+57,Psychology,0.91,7.70,74.8
58,Psychology,3.35,5.99,81.9
59,Business,12.20,7.20,81.9
60,Business,8.55,8.80,68.5
@@ -89,7 +89,7 @@ id,programme,stress,sleep_hours,exam_score
88,Psychology,0.81,8.65,100.0
89,Psychology,4.00,5.89,73.5
90,Business,2.06,7.59,88.8
-91,Business,40.00,7.57,69.3
+91,Business,15.96,8.29,81.9
92,Psychology,21.54,6.10,69.3
93,Business,13.72,8.90,70.7
94,Business,38.54,3.00,36.0
@@ -104,7 +104,7 @@ id,programme,stress,sleep_hours,exam_score
103,Business,20.74,6.45,77.1
104,Psychology,34.96,5.48,47.7
105,Business,0.79,6.17,80.1
-106,Business,40.00,6.46,70.9
+106,Business,0.33,7.65,91.7
107,Psychology,11.76,7.84,63.5
108,Psychology,16.28,6.55,71.6
109,Business,0.04,7.33,91.4
@@ -114,7 +114,7 @@ id,programme,stress,sleep_hours,exam_score
113,Business,14.81,7.90,75.0
114,Business,12.00,6.84,67.0
115,Business,10.47,5.90,96.0
-116,Business,40.00,5.63,71.6
+116,Business,4.36,6.70,90.2
117,Business,36.16,6.54,64.4
118,Psychology,6.63,5.33,69.5
119,Psychology,2.00,7.37,74.6
@@ -142,7 +142,7 @@ id,programme,stress,sleep_hours,exam_score
141,Business,27.93,6.63,64.4
142,Psychology,1.80,7.62,80.0
143,Psychology,1.46,7.44,97.8
-144,Business,40.00,7.01,41.0
+144,Business,18.25,7.66,52.3
145,Business,5.67,4.16,52.4
146,Business,2.20,7.15,76.4
147,Business,27.16,6.87,61.0
@@ -175,7 +175,7 @@ id,programme,stress,sleep_hours,exam_score
174,Psychology,10.12,5.30,63.5
175,Business,5.44,6.93,74.3
176,Psychology,3.73,8.25,71.8
-177,Business,40.00,6.03,73.2
+177,Business,8.22,6.99,89.8
178,Business,4.84,7.06,67.5
179,Business,4.44,6.13,71.1
180,Business,23.41,6.81,65.8
@@ -186,7 +186,7 @@ id,programme,stress,sleep_hours,exam_score
185,Business,1.75,5.94,87.5
186,Business,1.82,6.66,77.5
187,Business,5.01,5.96,89.8
-188,Business,40.00,6.10,48.8
+188,Business,5.46,7.13,66.8
189,Business,5.82,6.65,91.5
190,Business,0.70,4.84,75.4
191,Psychology,4.74,6.73,67.6
@@ -240,7 +240,7 @@ id,programme,stress,sleep_hours,exam_score
239,Psychology,6.86,7.13,56.2
240,Business,3.33,8.06,76.2
241,Business,4.09,7.20,77.7
-242,Psychology,40.00,3.89,40.0
+242,Psychology,24.42,4.35,48.2
243,Psychology,31.88,5.61,53.7
244,Psychology,18.10,7.07,80.4
245,Psychology,13.78,5.39,61.7
@@ -249,7 +249,7 @@ id,programme,stress,sleep_hours,exam_score
248,Business,13.71,6.97,59.5
249,Psychology,6.16,6.71,60.5
250,Business,5.23,8.12,91.2
-251,Psychology,40.00,7.43,69.9
+251,Psychology,30.11,7.73,75.0
252,Psychology,16.60,8.04,79.9
253,Psychology,6.17,7.98,79.6
254,Psychology,3.16,7.72,66.2
@@ -258,7 +258,7 @@ id,programme,stress,sleep_hours,exam_score
257,Business,12.27,8.39,75.2
258,Psychology,5.49,8.57,79.7
259,Business,9.88,7.16,77.9
-260,Psychology,40.00,5.36,66.3
+260,Psychology,11.77,6.21,81.1
261,Psychology,8.91,6.61,62.8
262,Psychology,0.11,7.40,69.5
263,Psychology,20.30,6.01,79.4
@@ -293,7 +293,7 @@ id,programme,stress,sleep_hours,exam_score
292,Business,9.81,5.98,68.7
293,Psychology,5.91,7.38,73.1
294,Psychology,1.89,5.14,71.8
-295,Psychology,40.00,6.54,62.2
+295,Psychology,8.34,7.49,78.7
296,Business,12.07,8.47,75.1
297,Business,26.99,6.31,68.9
298,Business,17.14,5.78,76.6
@@ -344,7 +344,7 @@ id,programme,stress,sleep_hours,exam_score
343,Psychology,6.09,7.17,81.5
344,Psychology,21.47,6.45,74.5
345,Psychology,1.19,7.17,82.5
-346,Business,40.00,4.98,75.1
+346,Business,5.89,6.00,92.9
347,Business,20.46,8.06,95.6
348,Psychology,13.57,7.00,75.3
349,Business,33.66,5.96,68.0
@@ -396,7 +396,7 @@ id,programme,stress,sleep_hours,exam_score
395,Business,10.43,7.88,79.6
396,Psychology,14.00,7.54,72.2
397,Psychology,16.00,8.42,65.1
-398,Psychology,40.00,7.08,47.8
+398,Psychology,12.93,7.89,61.9
399,Business,22.25,6.34,89.6
400,Business,26.42,5.86,84.6
401,Psychology,2.77,7.35,68.6
@@ -480,7 +480,7 @@ id,programme,stress,sleep_hours,exam_score
479,Psychology,7.00,6.48,68.2
480,Business,36.29,5.95,59.4
481,Business,0.92,5.42,51.7
-482,Business,40.00,6.28,72.6
+482,Business,29.37,6.60,78.2
483,Business,2.19,5.44,90.6
484,Psychology,27.38,5.86,69.0
485,Psychology,14.86,7.53,66.7
@@ -518,23 +518,23 @@ id,programme,stress,sleep_hours,exam_score
517,Psychology,12.19,6.43,83.0
518,Business,1.79,8.56,86.7
519,Business,6.24,6.03,56.8
-520,Business,40.00,5.04,50.2
+520,Business,15.26,5.79,63.1
521,Business,13.82,6.34,96.4
522,Business,18.71,7.66,65.0
523,Business,7.98,7.99,96.6
524,Business,21.04,5.49,71.1
-525,Psychology,40.00,5.66,51.4
+525,Psychology,2.77,6.78,70.8
526,Business,16.25,7.62,54.6
-527,Psychology,40.00,5.96,59.3
+527,Psychology,10.66,6.84,74.6
528,Business,14.12,5.72,55.8
529,Business,3.17,7.97,98.3
530,Psychology,2.59,6.22,67.4
531,Business,15.86,6.99,66.2
532,Business,4.53,7.14,73.0
533,Psychology,7.21,7.55,90.0
-534,Psychology,40.00,6.26,63.6
+534,Psychology,7.93,7.22,80.3
535,Business,2.87,5.45,56.3
-536,Business,40.00,6.78,59.3
+536,Business,2.58,7.90,78.8
537,Psychology,18.19,5.03,81.3
538,Business,24.26,6.86,73.5
539,Psychology,28.65,6.65,78.8
@@ -564,7 +564,7 @@ id,programme,stress,sleep_hours,exam_score
563,Business,15.35,6.55,69.4
564,Business,13.07,6.52,83.1
565,Business,5.31,8.13,71.6
-566,Psychology,40.00,4.73,70.4
+566,Psychology,6.54,5.73,87.9
567,Psychology,6.96,6.97,98.3
568,Psychology,1.77,7.53,84.9
569,Psychology,2.09,6.48,87.2
@@ -598,7 +598,7 @@ id,programme,stress,sleep_hours,exam_score
597,Psychology,33.81,5.07,49.0
598,Business,0.91,7.96,68.6
599,Psychology,0.79,7.78,77.1
-600,Psychology,40.00,4.72,64.3
+600,Psychology,4.35,5.79,82.9
601,Business,3.91,6.38,90.4
602,Psychology,16.40,6.30,68.6
603,Business,18.95,5.38,64.5
@@ -611,7 +611,7 @@ id,programme,stress,sleep_hours,exam_score
610,Business,19.90,6.80,74.0
611,Business,8.56,5.37,68.6
612,Psychology,1.75,5.99,84.8
-613,Psychology,40.00,6.82,60.9
+613,Psychology,2.08,7.96,80.7
614,Business,7.37,6.81,80.6
615,Business,12.28,7.64,71.4
616,Psychology,17.91,4.53,58.9
@@ -694,7 +694,7 @@ id,programme,stress,sleep_hours,exam_score
693,Business,0.65,6.59,81.1
694,Psychology,1.01,8.75,80.2
695,Psychology,8.71,6.53,45.2
-696,Psychology,40.00,5.29,46.1
+696,Psychology,4.84,6.35,64.5
697,Business,17.51,7.51,84.4
698,Psychology,30.94,6.99,37.5
699,Psychology,19.70,6.24,87.8
@@ -719,7 +719,7 @@ id,programme,stress,sleep_hours,exam_score
718,Business,12.25,5.44,57.3
719,Business,9.65,6.46,71.3
720,Business,11.56,6.37,79.8
-721,Psychology,40.00,6.35,53.2
+721,Psychology,0.45,7.54,73.9
722,Psychology,6.17,8.20,74.6
723,Psychology,2.34,6.48,86.6
724,Psychology,12.78,6.27,77.3
@@ -769,7 +769,7 @@ id,programme,stress,sleep_hours,exam_score
768,Business,3.51,6.37,81.1
769,Psychology,4.55,8.28,86.5
770,Psychology,1.18,8.34,79.0
-771,Business,40.00,5.40,35.9
+771,Business,8.43,6.34,52.3
772,Psychology,16.33,8.02,71.3
773,Business,1.36,6.44,66.9
774,Psychology,1.46,5.70,90.5
@@ -810,11 +810,11 @@ id,programme,stress,sleep_hours,exam_score
809,Business,1.43,7.57,86.2
810,Business,15.32,7.34,60.4
811,Business,16.11,6.91,64.4
-812,Business,40.00,5.70,54.0
+812,Business,4.92,6.75,72.3
813,Business,17.26,5.08,61.5
814,Business,17.98,8.37,74.6
815,Business,5.98,6.12,54.0
-816,Business,40.00,6.42,55.3
+816,Business,25.56,6.85,62.8
817,Psychology,2.21,8.10,65.5
818,Psychology,10.43,6.17,68.9
819,Business,6.43,6.85,90.3
@@ -823,7 +823,7 @@ id,programme,stress,sleep_hours,exam_score
822,Psychology,2.24,7.26,80.2
823,Business,9.29,5.73,69.6
824,Business,21.93,6.36,70.7
-825,Business,40.00,6.90,72.5
+825,Business,2.45,8.03,92.1
826,Business,11.68,6.83,72.2
827,Business,2.45,5.62,61.4
828,Psychology,0.50,6.63,74.6
@@ -841,10 +841,10 @@ id,programme,stress,sleep_hours,exam_score
840,Business,2.98,7.44,87.8
841,Psychology,12.75,9.37,83.0
842,Psychology,1.51,7.61,68.4
-843,Psychology,40.00,6.61,51.2
+843,Psychology,0.11,7.80,72.0
844,Psychology,8.64,7.12,54.5
845,Psychology,18.81,5.83,72.2
-846,Psychology,40.00,5.15,73.4
+846,Psychology,18.93,5.78,84.4
847,Business,22.38,7.67,63.2
848,Psychology,11.44,8.27,96.1
849,Business,6.34,5.97,72.8
@@ -860,10 +860,10 @@ id,programme,stress,sleep_hours,exam_score
859,Business,13.71,8.13,87.9
860,Business,24.78,7.15,44.7
861,Business,14.95,8.24,83.5
-862,Business,40.00,6.28,69.4
+862,Business,0.81,7.45,89.9
863,Business,5.06,6.26,80.5
864,Business,4.95,4.75,68.1
-865,Business,40.00,7.63,75.0
+865,Business,30.81,7.91,79.8
866,Business,30.21,7.56,55.2
867,Psychology,33.03,3.69,35.0
868,Psychology,3.30,6.79,66.4
@@ -887,14 +887,14 @@ id,programme,stress,sleep_hours,exam_score
886,Psychology,22.53,6.48,75.7
887,Business,23.59,4.99,73.2
888,Business,14.27,7.54,82.0
-889,Psychology,40.00,6.02,40.9
+889,Psychology,3.87,7.10,59.8
890,Psychology,38.16,4.45,49.0
891,Psychology,13.35,7.31,62.5
892,Psychology,34.57,4.25,45.4
893,Business,5.49,7.47,66.8
894,Business,0.01,5.99,91.5
895,Psychology,8.41,8.60,69.6
-896,Psychology,40.00,4.15,41.5
+896,Psychology,13.10,4.96,55.5
897,Business,25.06,6.63,84.3
898,Psychology,25.85,7.79,69.1
899,Business,24.84,7.55,71.6
@@ -903,7 +903,7 @@ id,programme,stress,sleep_hours,exam_score
902,Psychology,0.20,7.04,100.0
903,Business,0.16,8.00,90.7
904,Business,14.38,6.69,76.2
-905,Business,40.00,6.70,55.6
+905,Business,0.86,7.88,76.1
906,Psychology,5.31,7.25,69.1
907,Business,2.41,5.96,68.0
908,Psychology,34.04,6.03,57.8
@@ -916,7 +916,7 @@ id,programme,stress,sleep_hours,exam_score
915,Psychology,1.12,6.62,100.0
916,Psychology,2.24,8.97,68.2
917,Business,1.28,7.87,91.5
-918,Psychology,40.00,6.32,61.1
+918,Psychology,0.67,7.50,81.6
919,Business,30.32,6.31,59.3
920,Psychology,15.97,7.46,61.8
921,Business,9.10,9.70,75.7
@@ -931,7 +931,7 @@ id,programme,stress,sleep_hours,exam_score
930,Business,23.91,6.89,85.4
931,Business,2.25,7.22,88.6
932,Psychology,11.08,7.62,79.2
-933,Business,40.00,6.48,55.3
+933,Business,15.10,7.23,68.2
934,Business,8.27,7.43,60.1
935,Business,18.98,7.97,78.7
936,Psychology,4.31,5.39,77.4
@@ -948,7 +948,7 @@ id,programme,stress,sleep_hours,exam_score
947,Psychology,23.04,5.93,65.5
948,Business,9.42,7.29,72.2
949,Business,1.91,8.15,69.7
-950,Business,40.00,6.02,61.0
+950,Business,12.65,6.84,75.3
951,Business,15.87,7.33,43.7
952,Business,1.92,6.46,89.3
953,Business,5.40,8.69,66.2
@@ -961,7 +961,7 @@ id,programme,stress,sleep_hours,exam_score
960,Business,12.28,6.78,81.6
961,Business,17.09,6.23,66.5
962,Psychology,1.16,8.11,93.5
-963,Business,40.00,6.24,61.1
+963,Business,7.84,7.21,77.9
964,Psychology,8.16,6.05,76.8
965,Business,11.45,7.31,79.4
966,Psychology,6.82,6.97,49.3
@@ -987,10 +987,10 @@ id,programme,stress,sleep_hours,exam_score
986,Psychology,0.21,6.86,77.0
987,Psychology,0.07,6.34,69.3
988,Psychology,8.00,7.71,81.6
-989,Business,40.00,6.82,61.9
+989,Business,8.45,7.77,78.4
990,Business,29.38,6.37,77.6
991,Psychology,38.49,5.00,62.5
-992,Psychology,40.00,4.97,49.6
+992,Psychology,8.89,5.90,65.8
993,Psychology,9.61,6.72,73.8
994,Psychology,18.37,5.24,71.6
995,Psychology,23.76,6.39,67.7
@@ -1019,7 +1019,7 @@ id,programme,stress,sleep_hours,exam_score
1018,Psychology,10.34,7.34,81.9
1019,Business,3.23,7.04,78.3
1020,Psychology,26.50,4.93,77.9
-1021,Psychology,40.00,5.86,65.7
+1021,Psychology,9.68,6.77,81.5
1022,Psychology,5.57,9.10,100.0
1023,Business,8.90,5.58,63.6
1024,Business,11.23,6.28,82.9
@@ -1055,7 +1055,7 @@ id,programme,stress,sleep_hours,exam_score
1054,Business,15.33,5.37,61.2
1055,Business,30.44,8.13,61.6
1056,Business,3.83,7.94,88.2
-1057,Psychology,40.00,3.97,30.9
+1057,Psychology,9.64,4.88,46.8
1058,Business,3.88,8.04,81.5
1059,Psychology,12.46,5.54,67.2
1060,Business,6.74,6.13,71.1
@@ -1077,7 +1077,7 @@ id,programme,stress,sleep_hours,exam_score
1076,Psychology,9.68,5.84,77.0
1077,Business,13.88,8.69,77.3
1078,Business,0.16,9.47,77.4
-1079,Psychology,40.00,6.10,64.7
+1079,Psychology,3.15,7.21,84.0
1080,Psychology,5.76,8.10,65.1
1081,Psychology,4.49,7.53,82.5
1082,Psychology,10.27,6.25,74.3
@@ -1095,7 +1095,7 @@ id,programme,stress,sleep_hours,exam_score
1094,Business,11.23,8.47,70.8
1095,Business,19.51,6.46,79.4
1096,Business,0.10,5.85,67.3
-1097,Business,40.00,5.13,52.9
+1097,Business,10.58,6.01,68.2
1098,Psychology,5.48,7.32,60.6
1099,Business,0.50,7.95,75.0
1100,Psychology,14.06,8.10,65.2
@@ -1154,7 +1154,7 @@ id,programme,stress,sleep_hours,exam_score
1153,Business,27.02,5.67,80.1
1154,Business,3.50,6.49,70.5
1155,Business,2.56,7.50,82.0
-1156,Business,40.00,7.92,42.3
+1156,Business,6.09,8.94,60.0
1157,Business,5.42,8.85,82.5
1158,Business,17.93,6.33,81.6
1159,Psychology,1.36,7.76,78.7
@@ -1167,12 +1167,12 @@ id,programme,stress,sleep_hours,exam_score
1166,Business,1.99,8.57,85.8
1167,Psychology,4.64,8.06,74.4
1168,Business,14.14,5.99,71.4
-1169,Business,40.00,6.69,62.8
+1169,Business,19.19,7.32,73.7
1170,Psychology,5.03,7.02,79.4
1171,Business,0.81,7.57,70.9
1172,Psychology,8.01,7.48,84.7
1173,Psychology,18.37,4.27,72.7
-1174,Psychology,40.00,5.94,62.8
+1174,Psychology,12.77,6.76,77.1
1175,Business,16.57,6.74,84.0
1176,Business,22.95,7.08,66.6
1177,Business,10.15,6.43,83.2
@@ -1242,7 +1242,7 @@ id,programme,stress,sleep_hours,exam_score
1241,Psychology,5.59,8.62,92.1
1242,Psychology,11.30,7.99,84.4
1243,Business,3.79,6.31,75.1
-1244,Psychology,40.00,7.13,64.9
+1244,Psychology,1.29,8.29,85.1
1245,Business,5.43,7.03,66.7
1246,Psychology,0.72,4.97,92.3
1247,Psychology,37.73,3.58,67.3
@@ -1312,13 +1312,13 @@ id,programme,stress,sleep_hours,exam_score
1311,Business,10.85,8.13,88.8
1312,Psychology,19.54,7.32,50.9
1313,Business,5.48,9.04,73.1
-1314,Psychology,40.00,7.69,86.2
+1314,Psychology,8.68,8.63,100.0
1315,Business,9.21,7.24,80.2
1316,Business,8.58,8.05,82.0
1317,Business,16.29,5.71,68.2
1318,Business,0.57,6.98,68.5
1319,Business,1.63,7.91,56.4
-1320,Psychology,40.00,6.87,50.3
+1320,Psychology,14.25,7.65,63.8
1321,Psychology,1.15,7.67,76.3
1322,Business,9.85,7.11,82.9
1323,Psychology,19.15,6.90,67.1
@@ -1334,7 +1334,7 @@ id,programme,stress,sleep_hours,exam_score
1333,Psychology,6.20,7.75,77.1
1334,Business,6.92,7.40,100.0
1335,Business,11.82,6.77,65.9
-1336,Psychology,40.00,6.51,57.6
+1336,Psychology,4.70,7.57,76.0
1337,Business,14.21,8.46,68.7
1338,Psychology,24.49,7.17,77.2
1339,Psychology,4.73,6.64,89.4
@@ -1366,7 +1366,7 @@ id,programme,stress,sleep_hours,exam_score
1365,Business,29.19,6.56,89.3
1366,Psychology,20.36,7.40,83.2
1367,Business,2.43,7.96,68.6
-1368,Psychology,40.00,7.98,62.2
+1368,Psychology,0.15,9.17,83.0
1369,Psychology,29.41,6.21,70.0
1370,Psychology,7.32,5.27,98.1
1371,Psychology,2.17,7.27,80.9
@@ -1449,7 +1449,7 @@ id,programme,stress,sleep_hours,exam_score
1448,Business,19.97,8.18,53.8
1449,Psychology,26.63,6.91,89.9
1450,Business,1.08,4.81,52.9
-1451,Business,40.00,5.85,57.1
+1451,Business,8.67,6.79,73.5
1452,Business,5.20,7.18,83.7
1453,Business,8.24,8.61,78.5
1454,Business,18.24,7.11,79.1
@@ -1457,12 +1457,12 @@ id,programme,stress,sleep_hours,exam_score
1456,Psychology,11.04,7.93,83.5
1457,Psychology,33.47,3.61,56.2
1458,Business,5.21,7.14,61.2
-1459,Psychology,40.00,5.27,55.8
+1459,Psychology,10.52,6.16,71.2
1460,Business,6.13,8.86,100.0
1461,Business,31.66,4.91,58.7
1462,Business,21.39,5.95,53.2
1463,Business,7.04,7.05,82.2
-1464,Business,40.00,5.44,59.5
+1464,Business,1.65,6.59,79.5
1465,Psychology,3.99,6.90,80.4
1466,Business,4.06,6.10,80.5
1467,Business,0.16,6.52,78.5
@@ -1471,7 +1471,7 @@ id,programme,stress,sleep_hours,exam_score
1470,Psychology,15.71,6.04,63.3
1471,Business,3.02,8.38,91.2
1472,Psychology,18.74,6.77,82.4
-1473,Business,40.00,3.09,32.0
+1473,Business,5.55,4.12,50.0
1474,Business,13.96,6.71,76.4
1475,Business,7.54,8.20,87.0
1476,Business,36.77,3.94,49.9
@@ -1486,13 +1486,13 @@ id,programme,stress,sleep_hours,exam_score
1485,Business,15.06,8.56,82.2
1486,Business,16.72,8.77,77.9
1487,Business,10.36,6.70,73.7
-1488,Psychology,40.00,6.00,59.1
+1488,Psychology,8.35,6.95,75.7
1489,Business,0.46,7.23,66.1
1490,Business,30.67,7.18,53.1
1491,Psychology,9.09,6.60,57.9
1492,Business,10.06,7.70,85.8
1493,Psychology,5.66,7.85,80.3
-1494,Psychology,40.00,5.50,63.5
+1494,Psychology,16.68,6.20,75.6
1495,Business,24.87,6.64,50.0
1496,Business,5.27,7.55,74.5
1497,Business,0.46,5.80,71.1
@@ -1507,7 +1507,7 @@ id,programme,stress,sleep_hours,exam_score
1506,Business,5.50,9.24,80.9
1507,Psychology,12.71,7.87,73.1
1508,Psychology,35.15,5.14,67.0
-1509,Business,40.00,7.10,88.6
+1509,Business,16.26,7.81,100.0
1510,Business,10.00,6.60,84.9
1511,Psychology,6.16,7.15,82.9
1512,Business,7.83,7.82,74.2
@@ -1538,7 +1538,7 @@ id,programme,stress,sleep_hours,exam_score
1537,Psychology,24.12,4.74,75.5
1538,Psychology,10.74,7.27,52.9
1539,Psychology,15.99,6.93,66.1
-1540,Business,40.00,4.98,60.1
+1540,Business,0.38,6.17,80.8
1541,Psychology,10.82,7.49,58.3
1542,Psychology,33.03,6.16,59.0
1543,Psychology,3.32,8.06,52.3
@@ -1559,7 +1559,7 @@ id,programme,stress,sleep_hours,exam_score
1558,Psychology,3.83,7.56,82.8
1559,Psychology,0.24,7.30,62.5
1560,Psychology,9.76,7.50,78.7
-1561,Business,40.00,6.14,65.2
+1561,Business,3.96,7.22,84.0
1562,Psychology,25.95,5.79,65.0
1563,Business,0.60,5.33,73.7
1564,Business,25.55,5.69,54.6
@@ -1575,7 +1575,7 @@ id,programme,stress,sleep_hours,exam_score
1574,Psychology,13.06,7.67,75.0
1575,Psychology,17.69,5.03,76.3
1576,Psychology,11.85,6.43,71.6
-1577,Business,40.00,5.89,60.0
+1577,Business,0.97,7.07,80.4
1578,Business,1.02,6.25,75.9
1579,Business,7.40,7.84,68.8
1580,Business,4.10,6.39,85.0
@@ -1583,14 +1583,14 @@ id,programme,stress,sleep_hours,exam_score
1582,Business,22.68,6.07,65.5
1583,Business,14.66,9.10,80.9
1584,Psychology,2.06,7.99,85.3
-1585,Psychology,40.00,5.13,74.9
+1585,Psychology,10.98,6.00,90.0
1586,Psychology,9.14,4.75,64.2
1587,Business,0.61,6.66,78.5
1588,Business,7.44,7.43,71.6
1589,Business,0.67,6.98,67.9
1590,Psychology,14.93,5.63,57.3
1591,Business,23.23,6.38,81.1
-1592,Business,40.00,5.44,70.1
+1592,Business,9.83,6.34,85.9
1593,Psychology,33.07,5.40,63.6
1594,Psychology,2.62,7.23,90.3
1595,Business,3.02,5.28,69.2
@@ -1604,12 +1604,12 @@ id,programme,stress,sleep_hours,exam_score
1603,Psychology,11.59,6.11,63.8
1604,Business,2.67,8.40,90.5
1605,Business,1.56,6.01,73.4
-1606,Business,40.00,5.74,50.5
+1606,Business,5.22,6.78,68.7
1607,Business,8.04,6.40,62.6
-1608,Psychology,40.00,6.46,65.1
+1608,Psychology,5.02,7.51,83.3
1609,Psychology,1.28,5.95,88.5
1610,Business,30.85,6.24,49.1
-1611,Psychology,40.00,7.08,56.5
+1611,Psychology,23.89,7.57,64.9
1612,Business,0.56,8.56,76.4
1613,Psychology,4.04,6.37,58.4
1614,Business,7.54,8.54,62.8
@@ -1647,11 +1647,11 @@ id,programme,stress,sleep_hours,exam_score
1646,Business,18.92,8.27,60.8
1647,Psychology,12.97,7.28,63.1
1648,Business,18.57,6.99,76.2
-1649,Business,40.00,4.83,62.2
+1649,Business,8.18,5.78,78.8
1650,Business,19.87,6.44,76.8
1651,Psychology,3.99,6.89,63.3
1652,Psychology,5.07,7.29,71.0
-1653,Business,40.00,7.37,55.2
+1653,Business,2.80,8.49,74.6
1654,Business,4.27,6.62,59.4
1655,Psychology,2.55,6.75,78.8
1656,Psychology,11.78,6.63,56.6
@@ -1667,7 +1667,7 @@ id,programme,stress,sleep_hours,exam_score
1666,Psychology,4.35,5.87,66.8
1667,Business,18.69,7.66,73.5
1668,Business,11.70,6.45,74.8
-1669,Business,40.00,6.55,83.6
+1669,Business,11.04,7.41,98.7
1670,Psychology,1.37,6.61,100.0
1671,Psychology,4.79,7.05,77.2
1672,Psychology,3.24,5.99,80.9
@@ -1696,7 +1696,7 @@ id,programme,stress,sleep_hours,exam_score
1695,Psychology,8.41,5.59,83.9
1696,Business,10.66,7.37,80.5
1697,Psychology,2.41,8.57,75.4
-1698,Business,40.00,5.04,50.4
+1698,Business,15.20,5.79,63.4
1699,Psychology,24.51,6.45,53.1
1700,Psychology,25.21,7.67,69.3
1701,Business,19.52,9.05,72.1
@@ -1713,7 +1713,7 @@ id,programme,stress,sleep_hours,exam_score
1712,Psychology,3.19,8.98,87.7
1713,Psychology,24.97,7.25,69.4
1714,Psychology,0.21,9.09,90.5
-1715,Business,40.00,7.16,63.9
+1715,Business,3.36,8.26,83.0
1716,Psychology,38.06,7.64,69.6
1717,Business,5.72,5.81,67.7
1718,Psychology,2.19,5.59,57.0
@@ -1732,16 +1732,16 @@ id,programme,stress,sleep_hours,exam_score
1731,Business,3.24,5.71,67.3
1732,Business,11.52,5.07,68.3
1733,Business,16.87,6.85,68.2
-1734,Psychology,40.00,5.99,59.0
+1734,Psychology,6.23,7.01,76.6
1735,Psychology,13.44,6.31,76.7
-1736,Psychology,40.00,5.45,61.6
+1736,Psychology,2.84,6.56,81.0
1737,Psychology,19.94,5.51,58.4
-1738,Psychology,40.00,6.52,57.8
+1738,Psychology,12.77,7.34,72.0
1739,Psychology,6.98,6.82,76.0
1740,Business,24.67,5.33,69.4
1741,Psychology,3.30,6.48,80.4
1742,Psychology,9.36,5.93,70.2
-1743,Psychology,40.00,7.00,69.5
+1743,Psychology,0.30,8.19,90.2
1744,Psychology,5.80,5.90,88.3
1745,Business,35.87,5.70,52.0
1746,Psychology,4.30,8.43,81.7
@@ -1761,7 +1761,7 @@ id,programme,stress,sleep_hours,exam_score
1760,Psychology,4.22,9.06,59.8
1761,Psychology,7.83,7.90,94.2
1762,Business,24.69,5.96,71.5
-1763,Psychology,40.00,6.49,55.8
+1763,Psychology,11.89,7.34,70.5
1764,Business,10.49,6.11,63.7
1765,Psychology,30.24,6.80,72.1
1766,Psychology,2.71,7.64,82.1
@@ -1790,7 +1790,7 @@ id,programme,stress,sleep_hours,exam_score
1789,Psychology,1.41,8.21,72.8
1790,Psychology,37.09,6.36,57.9
1791,Business,11.49,8.05,88.2
-1792,Psychology,40.00,5.78,58.5
+1792,Psychology,1.41,6.94,78.6
1793,Psychology,2.51,7.20,96.8
1794,Psychology,4.12,8.76,80.5
1795,Business,9.53,6.35,70.1
@@ -1798,7 +1798,7 @@ id,programme,stress,sleep_hours,exam_score
1797,Business,8.31,8.77,87.8
1798,Business,9.99,8.76,66.1
1799,Psychology,13.40,7.44,74.0
-1800,Psychology,40.00,3.54,48.5
+1800,Psychology,1.69,4.69,68.5
1801,Psychology,14.38,8.75,69.0
1802,Business,17.78,8.08,56.6
1803,Psychology,17.03,6.76,65.8
@@ -1813,7 +1813,7 @@ id,programme,stress,sleep_hours,exam_score
1812,Psychology,21.15,7.74,73.6
1813,Business,16.21,7.84,57.9
1814,Business,2.90,4.79,61.1
-1815,Psychology,40.00,6.49,89.4
+1815,Psychology,24.34,6.96,97.6
1816,Psychology,5.16,5.97,57.5
1817,Psychology,4.26,7.15,79.2
1818,Psychology,20.08,6.14,58.9
@@ -1827,7 +1827,7 @@ id,programme,stress,sleep_hours,exam_score
1826,Psychology,12.13,7.57,59.8
1827,Psychology,3.60,6.68,87.3
1828,Business,2.97,8.68,84.8
-1829,Psychology,40.00,6.72,57.2
+1829,Psychology,0.52,7.91,77.8
1830,Business,5.75,7.67,61.8
1831,Psychology,14.67,6.64,72.0
1832,Psychology,18.97,6.27,50.6
@@ -1843,7 +1843,7 @@ id,programme,stress,sleep_hours,exam_score
1842,Business,22.92,7.96,63.0
1843,Business,14.90,6.22,63.7
1844,Psychology,12.51,7.01,76.5
-1845,Business,40.00,5.67,55.5
+1845,Business,11.73,6.52,70.2
1846,Business,23.05,5.27,56.2
1847,Business,10.27,6.80,60.6
1848,Business,25.75,5.88,55.9
@@ -1857,7 +1857,7 @@ id,programme,stress,sleep_hours,exam_score
1856,Psychology,2.48,7.68,78.4
1857,Business,2.21,7.75,92.6
1858,Business,18.87,7.50,66.9
-1859,Business,40.00,7.31,60.5
+1859,Business,5.70,8.34,78.4
1860,Business,0.22,5.98,67.5
1861,Business,10.82,7.31,76.4
1862,Business,0.01,6.91,80.5
@@ -1922,7 +1922,7 @@ id,programme,stress,sleep_hours,exam_score
1921,Business,6.53,6.57,82.6
1922,Psychology,9.63,5.97,82.9
1923,Business,2.12,6.86,99.1
-1924,Business,40.00,5.48,41.9
+1924,Business,4.35,6.55,60.5
1925,Business,21.99,7.53,68.2
1926,Business,3.94,7.17,81.9
1927,Business,2.09,8.13,86.5
@@ -1975,7 +1975,7 @@ id,programme,stress,sleep_hours,exam_score
1974,Business,8.25,7.42,79.6
1975,Psychology,19.03,6.59,81.0
1976,Business,38.27,6.51,58.1
-1977,Business,40.00,6.04,67.9
+1977,Business,5.64,7.07,85.9
1978,Business,29.91,6.37,45.5
1979,Business,1.12,5.94,79.7
1980,Psychology,14.58,6.71,54.1
@@ -2000,16 +2000,16 @@ id,programme,stress,sleep_hours,exam_score
1999,Psychology,18.41,6.48,76.6
2000,Psychology,21.42,4.88,73.9
2001,Psychology,9.15,4.82,81.4
-2002,Business,40.00,5.46,53.3
+2002,Business,1.40,6.62,73.5
2003,Psychology,3.82,8.04,78.3
2004,Business,10.67,7.27,50.8
2005,Psychology,9.21,7.85,80.1
2006,Business,19.17,5.54,66.4
-2007,Business,40.00,5.95,59.1
+2007,Business,3.57,7.04,78.1
2008,Psychology,2.63,5.36,54.9
2009,Business,36.26,5.77,76.0
2010,Business,7.07,7.51,81.5
-2011,Psychology,40.00,7.52,67.3
+2011,Psychology,21.40,8.07,77.0
2012,Psychology,10.08,7.14,78.0
2013,Business,6.84,6.96,51.7
2014,Business,11.46,7.61,53.1
@@ -2023,7 +2023,7 @@ id,programme,stress,sleep_hours,exam_score
2022,Psychology,10.79,6.79,65.6
2023,Psychology,17.92,7.71,79.6
2024,Psychology,14.32,7.31,61.8
-2025,Psychology,40.00,5.86,63.9
+2025,Psychology,4.52,6.93,82.4
2026,Business,11.43,8.32,97.7
2027,Business,2.11,9.04,89.8
2028,Business,10.48,7.48,73.4
@@ -2040,7 +2040,7 @@ id,programme,stress,sleep_hours,exam_score
2039,Psychology,9.91,7.96,60.0
2040,Psychology,2.65,7.87,73.4
2041,Business,11.08,6.40,78.8
-2042,Psychology,40.00,6.64,48.0
+2042,Psychology,9.58,7.55,63.9
2043,Business,0.23,4.66,53.5
2044,Business,30.78,8.16,73.5
2045,Psychology,5.08,8.13,84.9
@@ -2053,7 +2053,7 @@ id,programme,stress,sleep_hours,exam_score
2052,Business,0.40,8.30,76.8
2053,Business,12.89,6.48,73.8
2054,Psychology,0.91,7.94,75.3
-2055,Psychology,40.00,4.94,64.6
+2055,Psychology,10.37,5.83,80.0
2056,Business,6.01,6.31,78.4
2057,Psychology,4.84,6.75,77.2
2058,Business,19.08,5.14,65.8
@@ -2074,7 +2074,7 @@ id,programme,stress,sleep_hours,exam_score
2073,Business,3.13,4.38,82.1
2074,Psychology,0.54,6.47,90.1
2075,Psychology,7.81,6.02,66.4
-2076,Psychology,40.00,3.66,39.7
+2076,Psychology,3.07,4.76,59.0
2077,Psychology,24.06,5.63,93.7
2078,Business,5.74,10.33,61.4
2079,Psychology,0.93,6.50,80.4
@@ -2103,7 +2103,7 @@ id,programme,stress,sleep_hours,exam_score
2102,Business,22.40,7.28,76.1
2103,Psychology,5.39,6.80,79.3
2104,Psychology,7.38,8.14,69.0
-2105,Business,40.00,7.00,65.8
+2105,Business,5.92,8.02,83.6
2106,Business,12.04,7.13,73.8
2107,Business,12.58,7.90,82.1
2108,Psychology,14.75,3.90,62.8
@@ -2118,7 +2118,7 @@ id,programme,stress,sleep_hours,exam_score
2117,Business,16.78,7.00,82.5
2118,Business,8.15,6.77,49.1
2119,Business,3.51,8.73,83.3
-2120,Psychology,40.00,6.23,71.0
+2120,Psychology,4.51,7.29,89.5
2121,Psychology,23.79,6.61,74.3
2122,Business,3.89,8.06,79.5
2123,Business,10.11,8.19,98.7
@@ -2191,7 +2191,7 @@ id,programme,stress,sleep_hours,exam_score
2190,Business,0.21,6.00,81.4
2191,Psychology,11.35,6.54,71.9
2192,Business,6.76,6.21,69.3
-2193,Psychology,40.00,4.74,53.1
+2193,Psychology,6.46,5.74,70.6
2194,Psychology,8.49,8.50,64.1
2195,Business,3.33,6.13,73.2
2196,Psychology,11.28,7.01,83.7
@@ -2212,7 +2212,7 @@ id,programme,stress,sleep_hours,exam_score
2211,Psychology,10.92,7.66,68.1
2212,Business,3.67,5.80,74.5
2213,Psychology,12.32,6.48,90.3
-2214,Psychology,40.00,5.49,50.4
+2214,Psychology,0.31,6.68,71.1
2215,Psychology,1.62,8.11,87.7
2216,Business,29.41,6.58,68.0
2217,Business,31.57,6.44,72.6
@@ -2252,11 +2252,11 @@ id,programme,stress,sleep_hours,exam_score
2251,Psychology,0.63,6.92,89.8
2252,Psychology,11.58,6.49,72.4
2253,Psychology,20.16,6.42,73.8
-2254,Psychology,40.00,5.93,77.1
+2254,Psychology,28.03,6.29,83.4
2255,Business,10.26,6.85,77.2
2256,Business,4.03,6.66,77.4
2257,Business,19.70,6.77,74.2
-2258,Business,40.00,5.76,72.2
+2258,Business,3.44,6.85,91.2
2259,Business,24.67,6.68,98.6
2260,Psychology,32.26,7.65,59.3
2261,Psychology,10.97,6.53,67.7
@@ -2271,7 +2271,7 @@ id,programme,stress,sleep_hours,exam_score
2270,Business,17.45,5.06,85.6
2271,Business,21.79,6.96,70.7
2272,Business,17.97,7.66,88.8
-2273,Business,40.00,4.64,57.5
+2273,Business,1.75,5.79,77.5
2274,Business,0.81,8.86,83.8
2275,Psychology,19.18,7.21,72.5
2276,Business,16.65,7.22,76.0
@@ -2297,7 +2297,7 @@ id,programme,stress,sleep_hours,exam_score
2296,Business,8.87,7.40,71.5
2297,Business,12.55,6.37,57.6
2298,Business,17.77,6.78,100.0
-2299,Psychology,40.00,6.56,70.7
+2299,Psychology,6.61,7.57,88.2
2300,Business,23.52,4.69,51.9
2301,Psychology,22.64,6.70,80.9
2302,Psychology,2.49,8.62,70.1
@@ -2432,13 +2432,13 @@ id,programme,stress,sleep_hours,exam_score
2431,Business,4.80,6.18,79.5
2432,Psychology,9.94,7.85,65.7
2433,Business,7.53,6.66,67.8
-2434,Psychology,40.00,4.67,70.9
+2434,Psychology,1.43,5.82,91.1
2435,Business,5.17,5.13,71.9
2436,Psychology,32.82,7.27,59.7
2437,Psychology,19.16,6.34,73.5
2438,Business,27.67,6.26,69.0
2439,Business,39.79,8.90,55.5
-2440,Psychology,40.00,5.25,54.7
+2440,Psychology,21.53,5.80,64.3
2441,Psychology,6.32,5.39,74.7
2442,Psychology,7.25,7.62,66.8
2443,Business,2.04,6.85,98.9
@@ -2457,7 +2457,7 @@ id,programme,stress,sleep_hours,exam_score
2456,Business,4.81,5.18,88.7
2457,Business,3.16,5.09,75.1
2458,Business,13.17,7.49,83.0
-2459,Business,40.00,6.66,49.1
+2459,Business,30.35,6.95,54.2
2460,Business,27.14,6.51,66.0
2461,Psychology,8.32,8.70,91.4
2462,Business,12.63,7.57,87.9
@@ -2469,7 +2469,7 @@ id,programme,stress,sleep_hours,exam_score
2468,Business,0.80,6.43,52.2
2469,Psychology,7.82,8.47,83.0
2470,Business,5.04,6.46,85.2
-2471,Business,40.00,6.23,55.2
+2471,Business,4.94,7.28,73.5
2472,Business,20.30,4.22,50.7
2473,Business,12.39,7.03,57.7
2474,Psychology,7.11,6.76,75.4
@@ -2509,7 +2509,7 @@ id,programme,stress,sleep_hours,exam_score
2508,Business,1.90,7.56,99.7
2509,Psychology,0.14,8.76,90.9
2510,Business,2.12,7.36,78.9
-2511,Business,40.00,5.71,64.0
+2511,Business,5.61,6.74,82.0
2512,Business,3.62,8.11,78.8
2513,Business,22.85,6.87,75.1
2514,Psychology,25.79,7.26,74.7
@@ -2536,7 +2536,7 @@ id,programme,stress,sleep_hours,exam_score
2535,Psychology,28.59,6.29,69.4
2536,Business,1.43,7.02,100.0
2537,Psychology,5.53,8.26,67.6
-2538,Business,40.00,6.79,62.2
+2538,Business,0.21,7.99,82.9
2539,Psychology,26.80,8.41,55.4
2540,Business,10.32,6.67,68.8
2541,Business,12.45,7.10,68.9
@@ -2590,7 +2590,7 @@ id,programme,stress,sleep_hours,exam_score
2589,Psychology,4.13,7.57,96.8
2590,Business,24.77,7.40,71.7
2591,Psychology,16.42,4.57,72.1
-2592,Business,40.00,5.84,74.3
+2592,Business,7.76,6.80,91.1
2593,Psychology,30.56,6.76,71.5
2594,Psychology,6.23,7.86,83.4
2595,Business,4.24,5.62,78.4
@@ -2625,7 +2625,7 @@ id,programme,stress,sleep_hours,exam_score
2624,Business,5.63,6.77,81.4
2625,Psychology,22.27,5.87,74.3
2626,Psychology,21.33,8.47,100.0
-2627,Business,40.00,7.12,77.8
+2627,Business,20.22,7.72,88.1
2628,Business,24.54,6.35,71.5
2629,Psychology,13.66,5.55,82.2
2630,Psychology,5.79,6.90,54.8
@@ -2693,7 +2693,7 @@ id,programme,stress,sleep_hours,exam_score
2692,Business,25.94,5.79,63.4
2693,Psychology,0.77,8.16,66.7
2694,Psychology,13.13,7.63,80.6
-2695,Business,40.00,5.86,62.4
+2695,Business,14.59,6.63,75.7
2696,Psychology,1.83,6.55,84.0
2697,Psychology,9.61,7.52,61.2
2698,Psychology,1.22,7.91,82.8
@@ -2702,7 +2702,7 @@ id,programme,stress,sleep_hours,exam_score
2701,Psychology,20.83,8.17,78.9
2702,Business,10.37,5.25,86.0
2703,Psychology,14.72,8.14,65.7
-2704,Business,40.00,7.61,54.5
+2704,Business,3.03,8.72,73.8
2705,Psychology,6.68,8.13,98.0
2706,Psychology,15.19,8.67,60.6
2707,Psychology,0.66,8.45,95.7
@@ -2719,7 +2719,7 @@ id,programme,stress,sleep_hours,exam_score
2718,Business,6.00,5.64,65.5
2719,Business,39.50,4.69,54.3
2720,Business,4.41,7.94,64.8
-2721,Psychology,40.00,6.46,52.4
+2721,Psychology,24.25,6.93,60.7
2722,Business,7.36,7.44,75.8
2723,Business,0.84,7.36,84.8
2724,Psychology,1.45,7.57,75.8
@@ -2783,7 +2783,7 @@ id,programme,stress,sleep_hours,exam_score
2782,Psychology,3.08,7.92,74.8
2783,Psychology,1.39,7.04,76.3
2784,Psychology,38.00,5.26,52.5
-2785,Psychology,40.00,5.16,45.3
+2785,Psychology,15.23,5.90,58.2
2786,Psychology,1.67,8.44,84.5
2787,Psychology,8.45,7.19,85.5
2788,Psychology,1.48,6.16,83.2
@@ -2793,9 +2793,9 @@ id,programme,stress,sleep_hours,exam_score
2792,Psychology,7.09,8.03,82.4
2793,Psychology,5.44,8.21,81.0
2794,Business,28.50,6.81,54.4
-2795,Business,40.00,4.90,55.6
-2796,Business,40.00,4.50,49.4
-2797,Business,40.00,8.30,68.1
+2795,Business,5.81,5.92,73.4
+2796,Business,17.16,5.19,61.3
+2797,Business,18.36,8.95,79.4
2798,Psychology,5.89,8.09,79.9
2799,Psychology,28.15,5.83,71.7
2800,Psychology,11.09,6.42,63.2
@@ -2814,7 +2814,7 @@ id,programme,stress,sleep_hours,exam_score
2813,Psychology,21.69,4.95,64.8
2814,Psychology,7.72,5.66,56.7
2815,Business,3.17,6.48,63.7
-2816,Psychology,40.00,7.67,71.8
+2816,Psychology,14.10,8.44,85.3
2817,Psychology,4.12,7.97,66.7
2818,Business,6.58,5.87,77.2
2819,Business,5.27,8.40,73.9
@@ -2851,7 +2851,7 @@ id,programme,stress,sleep_hours,exam_score
2850,Psychology,33.04,7.51,70.7
2851,Psychology,18.56,5.11,54.4
2852,Psychology,12.34,7.13,68.0
-2853,Business,40.00,5.04,50.3
+2853,Business,4.38,6.11,68.9
2854,Business,8.13,7.62,89.2
2855,Psychology,17.78,7.33,68.5
2856,Business,26.50,6.02,71.3
@@ -2875,7 +2875,7 @@ id,programme,stress,sleep_hours,exam_score
2874,Business,0.06,7.26,69.6
2875,Psychology,3.96,7.90,88.8
2876,Psychology,8.61,6.55,72.1
-2877,Psychology,40.00,5.07,48.8
+2877,Psychology,1.67,6.22,68.9
2878,Psychology,25.67,7.87,62.5
2879,Business,0.36,6.29,82.9
2880,Psychology,14.10,6.73,70.4
@@ -2895,7 +2895,7 @@ id,programme,stress,sleep_hours,exam_score
2894,Business,28.40,6.85,88.0
2895,Psychology,29.38,6.66,62.4
2896,Business,8.11,6.61,58.8
-2897,Psychology,40.00,5.58,78.7
+2897,Psychology,10.58,6.46,94.1
2898,Business,8.25,8.04,67.1
2899,Business,0.14,8.42,71.2
2900,Psychology,25.48,6.30,75.1
@@ -2947,9 +2947,9 @@ id,programme,stress,sleep_hours,exam_score
2946,Business,18.92,6.89,62.4
2947,Psychology,1.19,7.29,83.5
2948,Psychology,31.08,6.08,57.0
-2949,Psychology,40.00,7.26,56.5
+2949,Psychology,32.84,7.48,60.2
2950,Business,8.50,7.16,72.2
-2951,Psychology,40.00,6.67,82.6
+2951,Psychology,1.17,7.83,100.0
2952,Psychology,5.72,8.53,92.1
2953,Psychology,18.19,6.43,83.0
2954,Business,14.59,6.28,54.4
@@ -2965,8 +2965,8 @@ id,programme,stress,sleep_hours,exam_score
2964,Psychology,8.35,7.68,75.6
2965,Business,1.30,7.43,83.2
2966,Psychology,1.10,7.35,100.0
-2967,Psychology,40.00,7.99,55.9
-2968,Business,40.00,4.43,65.1
+2967,Psychology,15.52,8.72,68.6
+2968,Business,21.93,4.97,74.5
2969,Psychology,5.68,6.51,81.2
2970,Business,32.56,5.51,64.5
2971,Psychology,15.04,6.02,71.2
@@ -3002,7 +3002,7 @@ id,programme,stress,sleep_hours,exam_score
3001,Psychology,17.24,5.93,71.7
3002,Psychology,9.03,8.39,94.8
3003,Business,2.23,6.82,92.2
-3004,Business,40.00,6.14,59.0
+3004,Business,0.29,7.33,79.7
3005,Psychology,4.33,7.41,86.0
3006,Business,1.69,6.22,77.4
3007,Psychology,5.46,6.50,78.0
@@ -3083,7 +3083,7 @@ id,programme,stress,sleep_hours,exam_score
3082,Psychology,1.41,5.37,75.0
3083,Business,13.26,7.47,82.9
3084,Business,21.35,8.08,63.2
-3085,Psychology,40.00,6.30,55.0
+3085,Psychology,6.47,7.31,72.6
3086,Business,14.84,6.35,63.7
3087,Psychology,1.90,7.39,96.0
3088,Business,24.50,7.14,69.1
@@ -3214,7 +3214,7 @@ id,programme,stress,sleep_hours,exam_score
3213,Psychology,17.45,7.22,78.8
3214,Psychology,3.40,6.38,62.1
3215,Psychology,5.38,7.23,84.3
-3216,Psychology,40.00,5.30,42.9
+3216,Psychology,7.45,6.28,59.9
3217,Business,0.71,8.73,82.5
3218,Business,3.96,5.16,71.7
3219,Business,6.81,6.43,75.3
@@ -3233,8 +3233,8 @@ id,programme,stress,sleep_hours,exam_score
3232,Business,5.96,5.70,94.3
3233,Business,0.21,7.20,77.1
3234,Business,11.91,5.91,66.0
-3235,Business,40.00,6.01,68.9
-3236,Psychology,40.00,5.40,79.9
+3235,Business,15.01,6.76,81.9
+3236,Psychology,2.02,6.54,99.7
3237,Business,13.13,4.33,46.8
3238,Business,5.57,6.03,81.5
3239,Psychology,6.11,7.66,86.7
@@ -3265,14 +3265,14 @@ id,programme,stress,sleep_hours,exam_score
3264,Business,26.64,5.64,83.1
3265,Business,6.35,6.29,63.3
3266,Business,7.81,6.94,82.3
-3267,Psychology,40.00,5.87,38.4
-3268,Business,40.00,7.42,58.1
+3267,Psychology,22.53,6.39,47.5
+3268,Business,1.87,8.56,78.0
3269,Business,8.57,6.04,55.9
3270,Psychology,7.06,5.76,71.4
3271,Psychology,10.16,8.09,80.4
3272,Business,4.53,5.78,82.5
3273,Psychology,4.57,5.10,78.3
-3274,Psychology,40.00,8.15,82.6
+3274,Psychology,3.70,9.24,100.0
3275,Psychology,1.79,7.00,74.3
3276,Psychology,26.92,6.42,60.9
3277,Psychology,12.65,7.67,63.7
@@ -3289,7 +3289,7 @@ id,programme,stress,sleep_hours,exam_score
3288,Business,19.69,6.09,89.6
3289,Psychology,17.22,8.60,82.9
3290,Psychology,6.99,5.90,82.5
-3291,Business,40.00,6.99,83.3
+3291,Business,2.66,8.11,100.0
3292,Psychology,6.70,5.75,82.5
3293,Psychology,1.66,5.69,76.6
3294,Business,4.37,7.68,85.7
@@ -3310,7 +3310,7 @@ id,programme,stress,sleep_hours,exam_score
3309,Business,2.12,8.18,84.7
3310,Business,0.46,6.87,80.4
3311,Business,16.52,5.39,66.1
-3312,Psychology,40.00,5.77,31.9
+3312,Psychology,34.25,5.94,34.9
3313,Business,31.85,7.20,61.8
3314,Business,3.28,6.36,64.6
3315,Psychology,15.53,6.63,82.6
@@ -3331,7 +3331,7 @@ id,programme,stress,sleep_hours,exam_score
3330,Psychology,5.28,5.41,80.5
3331,Psychology,21.57,7.08,67.5
3332,Business,8.26,7.36,71.4
-3333,Business,40.00,6.72,63.5
+3333,Business,11.66,7.57,78.3
3334,Business,1.31,6.37,71.1
3335,Psychology,21.14,5.19,69.8
3336,Business,22.60,4.95,48.2
@@ -3423,7 +3423,7 @@ id,programme,stress,sleep_hours,exam_score
3422,Psychology,0.88,8.15,97.0
3423,Psychology,7.48,5.08,70.6
3424,Psychology,9.18,6.53,71.2
-3425,Business,40.00,7.27,71.1
+3425,Business,15.91,8.00,83.7
3426,Business,3.23,6.08,86.8
3427,Psychology,16.38,7.18,65.6
3428,Business,7.08,8.27,76.3
@@ -3436,17 +3436,17 @@ id,programme,stress,sleep_hours,exam_score
3435,Psychology,6.44,5.37,53.8
3436,Business,13.74,8.75,72.0
3437,Psychology,3.19,7.01,61.8
-3438,Psychology,40.00,5.09,41.1
+3438,Psychology,4.85,6.14,59.4
3439,Psychology,17.91,6.23,68.8
3440,Business,3.39,6.74,86.1
3441,Business,4.16,7.53,66.5
-3442,Business,40.00,7.32,53.0
+3442,Business,27.30,7.70,59.7
3443,Business,0.12,6.71,91.8
3444,Business,6.63,6.87,90.5
3445,Psychology,6.85,6.27,71.5
3446,Business,3.74,5.30,73.5
3447,Psychology,28.73,5.88,62.9
-3448,Psychology,40.00,6.33,68.1
+3448,Psychology,13.70,7.12,81.8
3449,Business,18.37,6.33,76.2
3450,Psychology,4.65,8.98,86.3
3451,Psychology,2.71,8.21,72.7
@@ -3505,11 +3505,11 @@ id,programme,stress,sleep_hours,exam_score
3504,Psychology,7.81,5.29,72.5
3505,Business,12.26,6.19,69.4
3506,Psychology,4.68,7.90,88.8
-3507,Psychology,40.00,4.33,61.9
+3507,Psychology,4.48,5.40,80.4
3508,Psychology,0.61,7.34,75.0
3509,Business,2.00,8.24,72.6
3510,Business,8.78,9.10,73.2
-3511,Psychology,40.00,3.27,33.3
+3511,Psychology,23.99,3.76,41.7
3512,Business,15.21,6.43,61.8
3513,Psychology,3.84,6.18,76.3
3514,Psychology,26.70,5.96,57.8
@@ -3557,7 +3557,7 @@ id,programme,stress,sleep_hours,exam_score
3556,Psychology,1.60,7.41,82.8
3557,Business,18.89,6.70,84.7
3558,Business,3.19,9.82,98.7
-3559,Business,40.00,4.74,67.2
+3559,Business,6.59,5.74,84.7
3560,Business,3.11,5.23,69.6
3561,Psychology,12.28,5.31,83.6
3562,Psychology,3.70,7.21,95.4
@@ -3575,7 +3575,7 @@ id,programme,stress,sleep_hours,exam_score
3574,Business,10.41,7.00,77.2
3575,Business,4.91,6.70,82.0
3576,Business,8.08,5.86,73.9
-3577,Business,40.00,6.26,61.8
+3577,Business,17.85,6.92,73.3
3578,Business,1.07,7.09,80.5
3579,Business,30.97,5.59,56.0
3580,Psychology,19.92,8.01,73.3
@@ -3624,7 +3624,7 @@ id,programme,stress,sleep_hours,exam_score
3623,Business,0.33,8.48,64.1
3624,Psychology,16.12,4.80,60.1
3625,Psychology,25.68,7.49,82.4
-3626,Business,40.00,4.79,34.3
+3626,Business,20.42,5.38,44.5
3627,Psychology,0.46,8.27,87.8
3628,Business,1.43,6.21,76.6
3629,Psychology,19.46,7.13,54.5
@@ -3637,7 +3637,7 @@ id,programme,stress,sleep_hours,exam_score
3636,Business,8.09,8.11,74.7
3637,Business,37.26,7.72,66.5
3638,Psychology,5.29,7.39,70.7
-3639,Psychology,40.00,5.73,62.0
+3639,Psychology,9.88,6.63,77.7
3640,Psychology,19.63,6.85,79.5
3641,Psychology,5.51,6.25,80.1
3642,Business,3.30,5.28,82.4
@@ -3659,7 +3659,7 @@ id,programme,stress,sleep_hours,exam_score
3658,Business,13.65,6.01,74.5
3659,Psychology,0.12,7.16,54.5
3660,Business,0.04,8.64,72.5
-3661,Business,40.00,5.16,39.9
+3661,Business,4.39,6.23,58.5
3662,Business,8.42,7.35,68.2
3663,Psychology,15.79,6.54,77.5
3664,Psychology,27.19,6.48,59.7
@@ -3706,7 +3706,7 @@ id,programme,stress,sleep_hours,exam_score
3705,Psychology,1.56,5.78,79.4
3706,Psychology,0.25,7.63,84.1
3707,Psychology,6.63,6.93,83.2
-3708,Business,40.00,7.33,59.0
+3708,Business,20.67,7.91,69.1
3709,Business,4.33,5.99,82.5
3710,Business,3.32,6.91,45.5
3711,Psychology,2.63,9.90,92.5
@@ -3744,11 +3744,11 @@ id,programme,stress,sleep_hours,exam_score
3743,Psychology,13.98,5.91,83.4
3744,Psychology,11.08,8.13,64.6
3745,Psychology,4.99,6.82,64.2
-3746,Business,40.00,6.66,74.3
+3746,Business,0.87,7.84,94.7
3747,Business,3.95,7.53,58.4
3748,Psychology,9.43,6.92,88.5
3749,Psychology,0.10,7.79,95.1
-3750,Business,40.00,5.40,75.8
+3750,Business,4.12,6.47,94.5
3751,Psychology,19.92,5.01,69.3
3752,Business,22.67,5.90,68.0
3753,Business,1.07,6.57,72.1
@@ -3766,7 +3766,7 @@ id,programme,stress,sleep_hours,exam_score
3765,Business,4.52,7.99,79.3
3766,Psychology,19.45,8.31,71.4
3767,Psychology,8.75,6.73,87.3
-3768,Business,40.00,6.29,49.9
+3768,Business,3.68,7.38,68.9
3769,Psychology,22.11,6.43,72.9
3770,Psychology,0.81,7.24,72.4
3771,Psychology,7.96,5.63,72.5
@@ -3775,7 +3775,7 @@ id,programme,stress,sleep_hours,exam_score
3774,Business,9.40,6.19,74.5
3775,Business,0.72,6.25,78.0
3776,Psychology,8.98,8.00,80.0
-3777,Business,40.00,5.68,59.2
+3777,Business,31.66,5.93,63.6
3778,Psychology,5.16,6.85,81.7
3779,Psychology,2.62,6.70,63.4
3780,Business,2.78,5.24,99.8
@@ -3871,7 +3871,7 @@ id,programme,stress,sleep_hours,exam_score
3870,Psychology,16.00,6.04,85.1
3871,Business,1.90,7.80,77.1
3872,Business,3.22,7.35,60.3
-3873,Psychology,40.00,7.53,59.4
+3873,Psychology,7.01,8.52,76.7
3874,Business,19.45,5.95,59.0
3875,Psychology,29.34,3.95,69.4
3876,Business,1.99,8.90,82.4
@@ -3904,7 +3904,7 @@ id,programme,stress,sleep_hours,exam_score
3903,Psychology,1.62,7.11,83.5
3904,Business,6.47,8.66,76.1
3905,Business,0.22,9.00,75.3
-3906,Psychology,40.00,5.26,35.8
+3906,Psychology,30.21,5.55,40.9
3907,Psychology,14.50,7.18,80.4
3908,Psychology,22.45,5.57,46.1
3909,Psychology,1.63,5.69,71.6
@@ -3953,7 +3953,7 @@ id,programme,stress,sleep_hours,exam_score
3952,Business,3.24,8.86,78.9
3953,Business,13.18,5.97,84.9
3954,Psychology,2.29,5.32,78.5
-3955,Business,40.00,5.88,59.1
+3955,Business,26.61,6.29,66.1
3956,Psychology,16.85,7.18,68.4
3957,Business,5.59,5.45,67.2
3958,Business,8.75,5.75,74.7
@@ -3975,8 +3975,8 @@ id,programme,stress,sleep_hours,exam_score
3974,Business,29.90,5.54,57.9
3975,Psychology,9.45,6.66,71.0
3976,Psychology,0.98,7.01,80.6
-3977,Psychology,40.00,6.46,63.9
-3978,Psychology,40.00,6.97,51.9
+3977,Psychology,24.75,6.91,71.8
+3978,Psychology,3.10,8.07,71.2
3979,Psychology,0.05,4.60,65.2
3980,Psychology,31.51,5.95,73.2
3981,Business,37.18,4.92,58.7
@@ -3989,11 +3989,11 @@ id,programme,stress,sleep_hours,exam_score
3988,Psychology,7.89,8.29,78.9
3989,Business,5.64,7.11,81.5
3990,Business,1.25,7.91,77.1
-3991,Psychology,40.00,5.34,51.6
+3991,Psychology,0.17,6.54,72.4
3992,Psychology,1.62,7.03,73.2
3993,Psychology,15.97,5.40,68.7
3994,Business,3.95,8.31,91.7
-3995,Business,40.00,4.70,57.9
+3995,Business,7.44,5.67,74.9
3996,Psychology,10.03,8.26,81.5
3997,Business,4.13,8.95,76.2
3998,Business,22.91,7.50,67.1
@@ -4026,7 +4026,7 @@ id,programme,stress,sleep_hours,exam_score
4025,Business,10.91,7.29,71.8
4026,Psychology,1.54,7.70,74.4
4027,Psychology,23.15,6.53,53.0
-4028,Business,40.00,6.71,74.5
+4028,Business,1.01,7.88,94.8
4029,Business,1.93,6.59,74.1
4030,Psychology,9.79,8.28,79.0
4031,Business,0.49,6.02,77.4
@@ -4039,7 +4039,7 @@ id,programme,stress,sleep_hours,exam_score
4038,Psychology,17.93,7.87,74.5
4039,Business,1.99,4.93,60.3
4040,Business,3.88,6.29,83.5
-4041,Psychology,40.00,7.29,76.1
+4041,Psychology,1.17,8.46,96.4
4042,Psychology,0.16,6.92,65.6
4043,Business,16.33,7.58,89.0
4044,Psychology,1.69,5.67,91.9
@@ -4085,7 +4085,7 @@ id,programme,stress,sleep_hours,exam_score
4084,Business,10.44,5.66,71.1
4085,Business,19.45,4.41,56.9
4086,Business,6.34,6.48,77.2
-4087,Psychology,40.00,7.23,49.8
+4087,Psychology,20.44,7.82,60.0
4088,Business,2.11,8.37,96.2
4089,Psychology,4.35,6.40,77.5
4090,Business,4.35,6.44,59.3
@@ -4135,7 +4135,7 @@ id,programme,stress,sleep_hours,exam_score
4134,Business,23.74,6.42,59.9
4135,Psychology,3.82,6.36,61.6
4136,Psychology,4.08,7.44,64.6
-4137,Psychology,40.00,5.03,68.9
+4137,Psychology,0.11,6.22,89.7
4138,Business,0.44,5.45,77.6
4139,Business,26.05,7.44,82.8
4140,Psychology,0.48,5.92,73.7
@@ -4144,7 +4144,7 @@ id,programme,stress,sleep_hours,exam_score
4143,Business,2.79,6.74,80.5
4144,Psychology,19.19,7.18,48.2
4145,Psychology,5.05,8.69,70.7
-4146,Psychology,40.00,6.26,50.5
+4146,Psychology,36.76,6.35,52.2
4147,Business,2.47,9.32,79.8
4148,Psychology,0.89,5.96,88.5
4149,Business,5.42,6.67,90.6
@@ -4156,7 +4156,7 @@ id,programme,stress,sleep_hours,exam_score
4155,Business,11.70,6.16,71.1
4156,Business,1.68,7.74,83.3
4157,Business,16.44,6.49,68.0
-4158,Psychology,40.00,5.31,79.6
+4158,Psychology,13.79,6.10,93.3
4159,Business,24.77,4.11,48.9
4160,Business,4.94,6.01,72.3
4161,Psychology,8.69,4.90,57.2
@@ -4239,7 +4239,7 @@ id,programme,stress,sleep_hours,exam_score
4238,Psychology,8.61,6.88,78.4
4239,Psychology,6.37,4.90,67.6
4240,Business,7.01,7.25,100.0
-4241,Psychology,40.00,5.51,56.3
+4241,Psychology,6.69,6.51,73.7
4242,Psychology,10.53,6.96,93.1
4243,Psychology,26.19,6.58,60.6
4244,Business,13.05,6.13,98.7
@@ -4259,7 +4259,7 @@ id,programme,stress,sleep_hours,exam_score
4258,Psychology,2.36,6.59,77.5
4259,Psychology,1.43,8.30,92.2
4260,Psychology,7.46,7.51,78.5
-4261,Psychology,40.00,7.38,77.7
+4261,Psychology,0.50,8.57,98.3
4262,Psychology,21.92,6.20,74.2
4263,Psychology,12.46,5.58,66.4
4264,Psychology,0.06,8.92,73.4
@@ -4271,7 +4271,7 @@ id,programme,stress,sleep_hours,exam_score
4270,Business,8.19,8.74,94.9
4271,Business,4.45,6.18,63.8
4272,Psychology,7.22,7.18,50.7
-4273,Business,40.00,5.93,61.3
+4273,Business,36.04,6.05,63.4
4274,Business,0.84,7.25,81.6
4275,Psychology,0.04,7.17,95.6
4276,Business,7.07,9.13,84.0
@@ -4288,7 +4288,7 @@ id,programme,stress,sleep_hours,exam_score
4287,Business,23.85,8.55,76.5
4288,Business,20.15,6.47,57.3
4289,Psychology,11.73,7.13,85.6
-4290,Business,40.00,4.83,56.0
+4290,Business,12.97,5.64,70.1
4291,Business,1.40,6.98,78.2
4292,Psychology,4.78,5.72,56.4
4293,Business,0.77,6.45,81.5
@@ -4303,7 +4303,7 @@ id,programme,stress,sleep_hours,exam_score
4302,Business,8.96,6.42,76.7
4303,Business,4.88,8.99,76.8
4304,Psychology,27.80,7.27,61.4
-4305,Business,40.00,7.64,68.0
+4305,Business,17.06,8.33,80.0
4306,Business,6.16,6.61,68.7
4307,Psychology,15.11,6.34,82.0
4308,Psychology,34.64,7.04,64.1
@@ -4343,7 +4343,7 @@ id,programme,stress,sleep_hours,exam_score
4342,Business,19.10,5.17,81.6
4343,Psychology,35.95,5.78,60.4
4344,Business,16.07,6.51,71.0
-4345,Business,40.00,6.32,72.3
+4345,Business,1.22,7.49,92.5
4346,Psychology,7.73,7.90,76.8
4347,Business,3.89,6.09,93.4
4348,Business,2.86,7.56,73.2
@@ -4354,7 +4354,7 @@ id,programme,stress,sleep_hours,exam_score
4353,Business,7.04,6.58,55.7
4354,Business,10.03,4.49,74.5
4355,Psychology,29.57,5.80,63.7
-4356,Psychology,40.00,4.89,64.2
+4356,Psychology,9.37,5.81,80.1
4357,Business,9.89,5.56,63.9
4358,Business,15.26,6.76,78.7
4359,Business,20.06,7.02,68.5
@@ -4368,7 +4368,7 @@ id,programme,stress,sleep_hours,exam_score
4367,Business,2.49,8.46,68.8
4368,Business,5.63,8.23,68.4
4369,Business,1.16,6.92,61.7
-4370,Business,40.00,7.36,75.6
+4370,Business,4.00,8.44,94.4
4371,Business,8.72,6.73,52.9
4372,Business,4.32,7.57,72.1
4373,Business,10.77,8.07,66.9
@@ -4378,7 +4378,7 @@ id,programme,stress,sleep_hours,exam_score
4377,Psychology,2.94,6.88,60.7
4378,Psychology,0.49,6.19,84.3
4379,Psychology,8.98,6.07,59.7
-4380,Business,40.00,6.43,45.7
+4380,Business,14.64,7.19,58.9
4381,Business,0.88,8.52,69.3
4382,Business,12.21,8.61,80.6
4383,Business,26.83,6.30,69.1
@@ -4466,7 +4466,7 @@ id,programme,stress,sleep_hours,exam_score
4465,Business,12.67,8.67,62.4
4466,Business,0.37,6.45,86.4
4467,Business,16.52,7.02,78.4
-4468,Psychology,40.00,6.97,80.9
+4468,Psychology,3.26,8.07,100.0
4469,Psychology,2.93,7.45,80.9
4470,Psychology,18.05,6.88,79.0
4471,Business,8.77,4.47,78.5
@@ -4484,7 +4484,7 @@ id,programme,stress,sleep_hours,exam_score
4483,Psychology,10.67,8.68,69.6
4484,Business,6.55,6.53,73.7
4485,Psychology,12.60,6.96,60.5
-4486,Psychology,40.00,6.00,65.3
+4486,Psychology,3.36,7.09,84.4
4487,Business,10.43,7.76,73.9
4488,Psychology,5.98,6.64,79.7
4489,Business,11.26,6.60,79.7
@@ -4499,7 +4499,7 @@ id,programme,stress,sleep_hours,exam_score
4498,Business,12.01,7.13,72.7
4499,Business,1.92,7.03,78.3
4500,Business,3.90,5.53,77.3
-4501,Business,40.00,6.98,69.1
+4501,Business,6.92,7.97,86.4
4502,Psychology,13.43,7.13,81.3
4503,Psychology,13.10,5.99,61.5
4504,Business,31.78,3.61,72.5
@@ -4527,7 +4527,7 @@ id,programme,stress,sleep_hours,exam_score
4526,Business,3.70,6.07,93.8
4527,Psychology,10.05,6.73,79.0
4528,Psychology,20.34,7.28,63.7
-4529,Psychology,40.00,5.86,61.4
+4529,Psychology,4.16,6.94,80.1
4530,Business,4.31,7.94,77.2
4531,Business,3.11,6.48,77.4
4532,Psychology,37.48,7.44,44.3
@@ -4549,7 +4549,7 @@ id,programme,stress,sleep_hours,exam_score
4548,Business,3.35,8.60,91.5
4549,Psychology,3.29,8.54,90.8
4550,Business,4.16,8.99,72.9
-4551,Business,40.00,6.85,76.7
+4551,Business,39.29,6.87,77.1
4552,Business,13.64,6.78,93.3
4553,Business,12.03,7.95,69.8
4554,Business,25.26,8.19,79.9
@@ -4645,7 +4645,7 @@ id,programme,stress,sleep_hours,exam_score
4644,Psychology,16.13,6.40,77.6
4645,Business,20.70,5.84,80.2
4646,Business,2.30,7.48,88.5
-4647,Business,40.00,4.48,58.1
+4647,Business,6.84,5.48,75.5
4648,Psychology,0.88,9.37,100.0
4649,Psychology,10.45,5.48,65.8
4650,Psychology,2.93,7.70,73.1
@@ -4697,10 +4697,10 @@ id,programme,stress,sleep_hours,exam_score
4696,Business,8.28,7.60,83.5
4697,Business,8.33,6.07,71.1
4698,Psychology,0.20,7.89,77.4
-4699,Business,40.00,6.24,67.2
+4699,Business,2.85,7.35,86.6
4700,Psychology,32.31,6.25,76.4
4701,Psychology,5.00,6.34,72.2
-4702,Business,40.00,5.04,39.0
+4702,Business,3.13,6.15,58.2
4703,Business,3.52,7.66,93.3
4704,Psychology,12.95,9.28,98.0
4705,Business,15.23,8.27,83.3
@@ -4723,7 +4723,7 @@ id,programme,stress,sleep_hours,exam_score
4722,Business,11.16,6.57,88.1
4723,Business,8.79,6.18,80.9
4724,Business,2.35,6.65,75.1
-4725,Psychology,40.00,5.19,61.0
+4725,Psychology,2.83,6.31,80.4
4726,Business,18.52,7.17,51.9
4727,Psychology,5.17,5.64,71.4
4728,Business,4.34,6.84,68.5
@@ -4737,7 +4737,7 @@ id,programme,stress,sleep_hours,exam_score
4736,Business,1.62,7.00,69.3
4737,Business,0.96,6.02,80.7
4738,Business,2.48,7.35,82.4
-4739,Psychology,40.00,5.70,42.5
+4739,Psychology,3.06,6.81,61.7
4740,Business,3.86,8.38,73.6
4741,Business,2.54,6.82,80.5
4742,Psychology,0.28,5.85,87.0
@@ -4750,7 +4750,7 @@ id,programme,stress,sleep_hours,exam_score
4749,Business,22.54,6.15,78.0
4750,Business,7.34,6.53,58.7
4751,Psychology,8.34,7.32,65.9
-4752,Psychology,40.00,6.15,56.1
+4752,Psychology,14.80,6.91,69.2
4753,Psychology,0.31,6.52,88.3
4754,Business,12.29,6.06,62.9
4755,Psychology,10.02,5.94,72.1
@@ -4777,7 +4777,7 @@ id,programme,stress,sleep_hours,exam_score
4776,Psychology,8.30,7.27,74.6
4777,Psychology,5.44,7.69,70.6
4778,Psychology,3.05,8.36,67.4
-4779,Business,40.00,6.95,51.7
+4779,Business,16.78,7.64,63.8
4780,Business,1.09,6.40,72.5
4781,Psychology,1.07,7.68,73.6
4782,Psychology,6.14,6.20,66.9
@@ -4845,7 +4845,7 @@ id,programme,stress,sleep_hours,exam_score
4844,Business,20.53,5.71,69.3
4845,Business,6.17,7.12,74.4
4846,Business,27.46,7.56,63.3
-4847,Psychology,40.00,8.50,57.9
+4847,Psychology,17.43,9.18,69.6
4848,Business,6.47,7.16,85.6
4849,Psychology,8.28,5.91,79.9
4850,Business,3.71,6.74,76.4
@@ -4939,14 +4939,14 @@ id,programme,stress,sleep_hours,exam_score
4938,Psychology,0.39,7.65,80.1
4939,Psychology,6.05,6.93,75.0
4940,Psychology,4.19,7.58,96.1
-4941,Psychology,40.00,5.11,58.4
+4941,Psychology,0.90,6.29,78.8
4942,Business,12.46,7.48,81.2
4943,Psychology,21.84,7.10,70.5
4944,Business,2.37,8.73,61.8
4945,Business,5.16,7.20,80.4
4946,Psychology,5.36,8.32,73.0
4947,Business,4.78,7.79,70.7
-4948,Psychology,40.00,5.66,64.4
+4948,Psychology,5.82,6.69,82.2
4949,Psychology,0.81,6.64,77.1
4950,Business,17.41,4.76,49.5
4951,Business,7.90,6.27,76.3
@@ -4985,7 +4985,7 @@ id,programme,stress,sleep_hours,exam_score
4984,Psychology,2.34,6.02,91.5
4985,Business,32.54,7.40,57.0
4986,Business,20.40,5.46,55.4
-4987,Business,40.00,6.18,53.7
+4987,Business,29.04,6.51,59.4
4988,Psychology,8.65,8.02,81.1
4989,Business,27.27,6.29,78.8
4990,Psychology,13.69,5.27,74.3
diff --git a/scripts/generate-datasets.mjs b/scripts/generate-datasets.mjs
index 7843b7f..c5693c7 100644
--- a/scripts/generate-datasets.mjs
+++ b/scripts/generate-datasets.mjs
@@ -35,7 +35,10 @@ function writeWellbeingPopulation() {
for (let i = 1; i <= N; i += 1) {
const programme = rng() < 0.5 ? 'Psychology' : 'Business';
// Stress is skewed: most students low, a long tail of very stressed ones.
- const stress = Math.min(40, -12 * Math.log(Math.max(rng(), Number.EPSILON)));
+ // The scale runs 0 to 40, like the Perceived Stress Scale. Wrapping a draw
+ // past 40 back round to the start keeps the exponential shape inside the
+ // scale (it is memoryless), where clipping piled 190 students onto 40.
+ const stress = (-12 * Math.log(Math.max(rng(), Number.EPSILON))) % 40;
const sleep = Math.min(11, Math.max(3, normal(rng, 7.2 - stress * 0.03, 1.1)));
const exam = Math.min(100, Math.max(0, normal(rng, 62 + sleep * 2.4 - stress * 0.45, 11)));
rows.push([i, programme, stress.toFixed(2), sleep.toFixed(2), exam.toFixed(1)].join(','));
diff --git a/src/content/exercises/module-05.ts b/src/content/exercises/module-05.ts
index fac1201..4c25db7 100644
--- a/src/content/exercises/module-05.ts
+++ b/src/content/exercises/module-05.ts
@@ -38,10 +38,10 @@ export const module05: ExerciseDef[] = [
population <- read.csv("data/wellbeing-population.csv")
mu <- mean(population$exam_score)
sigma <- sd(population$exam_score)
- expected <- pnorm(60, mean = mu, sd = sigma) # 0.140774
+ expected <- pnorm(60, mean = mu, sd = sigma) # 0.125920
# tolerance 1e-3, not 1e-6: a student who computes the SD with denominator N
- # rather than sd()'s n - 1 lands on 0.140750 - the same answer to every digit
- # anyone would report. The three wrong answers are 0.859, 0.018 and 1.000,
+ # rather than sd()'s n - 1 lands on 0.125896 - the same answer to every digit
+ # anyone would report. The three wrong answers are 0.874, 0.017 and 1.000,
# all far outside this band.
if (isTRUE(all.equal(value, expected, tolerance = 1e-3, check.attributes = FALSE))) {
list(pass = TRUE, message = paste0("Correct: ", round(expected, 4), ". Under this normal model about ", round(100 * expected), " out of every 100 students score below 60, and the actual count in the population is ", sum(population$exam_score < 60), " out of 5000 - the model is close, not exact."))
@@ -99,10 +99,10 @@ export const module05: ExerciseDef[] = [
population <- read.csv("data/wellbeing-population.csv")
mu <- mean(population$exam_score)
sigma <- sd(population$exam_score)
- expected <- (85 - mu) / sigma # 0.946517
+ expected <- (85 - mu) / sigma # 0.916170
# tolerance 1e-3 for the same reason as m5-1-a: an SD computed with
- # denominator N gives 0.946612, which rounds identically at two decimals.
- # The wrong answers are 11.69, 6.88 and -0.95.
+ # denominator N gives 0.916262, which rounds identically at two decimals.
+ # The wrong answers are 11.11, 7.01 and -0.92.
if (isTRUE(all.equal(value, expected, tolerance = 1e-3, check.attributes = FALSE))) {
list(pass = TRUE, message = paste0("Correct: z = ", round(expected, 2), ". That student is just under one standard deviation above the mean, which puts them above about ", round(100 * pnorm(expected)), " per cent of students."))
} else if (isTRUE(all.equal(value, -expected, tolerance = 1e-3, check.attributes = FALSE))) {
@@ -155,8 +155,8 @@ export const module05: ExerciseDef[] = [
list(pass = FALSE, message = "Both z_exam and z_sleep should be single numbers.")
} else {
population <- read.csv("data/wellbeing-population.csv")
- want_exam <- (85 - mean(population$exam_score)) / sd(population$exam_score) # 0.946517
- want_sleep <- (9.1 - mean(population$sleep_hours)) / sd(population$sleep_hours) # 1.996967
+ want_exam <- (85 - mean(population$exam_score)) / sd(population$exam_score) # 0.916170
+ want_sleep <- (9.1 - mean(population$sleep_hours)) / sd(population$sleep_hours) # 1.986021
# tolerance 1e-3 throughout, as in m5-2-a: an SD computed with denominator N
# is within 1e-4 of sd(), and no wrong answer here is closer than 0.25.
ok_exam <- isTRUE(all.equal(z_exam, want_exam, tolerance = 1e-3, check.attributes = FALSE))
@@ -219,9 +219,9 @@ export const module05: ExerciseDef[] = [
population <- read.csv("data/wellbeing-population.csv")
mu <- mean(population$exam_score)
sigma <- sd(population$exam_score)
- expected <- qnorm(0.90, mean = mu, sd = sigma) # 89.13958
- # tolerance 1e-4: an SD computed with denominator N gives 89.13800, a
- # relative difference of 1.8e-5. The wrong answers are 57.5, 1.28 and
+ expected <- qnorm(0.90, mean = mu, sd = sigma) # 89.42980
+ # tolerance 1e-4: an SD computed with denominator N gives 89.42825, a
+ # relative difference of 1.7e-5. The wrong answers are 58.4, 1.28 and
# essentially 0, so nothing plausible sneaks through this band.
if (isTRUE(all.equal(value, expected, tolerance = 1e-4, check.attributes = FALSE))) {
list(pass = TRUE, message = paste0("Correct: ", round(expected, 2), ". In the actual population ", sum(population$exam_score > expected), " of 5000 students score above it - close to the 500 the model predicts."))
@@ -281,8 +281,8 @@ export const module05: ExerciseDef[] = [
sigma <- sd(population$exam_score)
lower <- pnorm(65, mean = mu, sd = sigma)
upper <- pnorm(85, mean = mu, sd = sigma)
- expected <- upper - lower # 0.577321
- # tolerance 1e-3, as in m5-1-a: the denominator-N SD gives 0.577290.
+ expected <- upper - lower # 0.588578
+ # tolerance 1e-3, as in m5-1-a: the denominator-N SD gives 0.588624.
if (isTRUE(all.equal(value, expected, tolerance = 1e-3, check.attributes = FALSE))) {
list(pass = TRUE, message = paste0("Correct: ", round(expected, 4), ". Just under three students in five fall in that twenty-point band, and the actual population count is ", sum(population$exam_score > 65 & population$exam_score < 85), " of 5000."))
} else if (value > 1) {
diff --git a/src/content/exercises/module-06.ts b/src/content/exercises/module-06.ts
index a8d2dd9..9920dcd 100644
--- a/src/content/exercises/module-06.ts
+++ b/src/content/exercises/module-06.ts
@@ -187,7 +187,7 @@ export const module06: ExerciseDef[] = [
expected <- sigma / sqrt(40)
# 1e-3 rather than 1e-6: admits a population SD computed with denominator N
# instead of sd()'s n - 1, which differs by ~1e-4 here. Both wrong answers
- # below (sigma ~10.6, sigma/40 ~0.27) are far outside this band.
+ # below (sigma ~9.2, sigma/40 ~0.23) are far outside this band.
# check.attributes = FALSE on each comparison: a second guard, so names never pick the wrong branch.
if (isTRUE(all.equal(value, expected, tolerance = 1e-3, check.attributes = FALSE))) {
list(pass = TRUE, message = paste0("Correct: ", round(expected, 3), ". Individual students vary by about ", round(sigma, 2), ", but sample means of 40 vary by only ", round(expected, 3), "."))
diff --git a/src/content/exercises/module-07.ts b/src/content/exercises/module-07.ts
index 6680b4a..7e72467 100644
--- a/src/content/exercises/module-07.ts
+++ b/src/content/exercises/module-07.ts
@@ -122,7 +122,7 @@ export const module07: ExerciseDef[] = [
# sort(): an interval written upper-first is the same interval.
value <- sort(value)
if (isTRUE(all.equal(value, expected, tolerance = 1e-6, check.attributes = FALSE))) {
- list(pass = TRUE, message = paste0("Correct: [", round(expected[1], 2), ", ", round(expected[2], 2), "]. The population mean is 73.31, so this interval does contain it - which about 19 intervals in 20 will."))
+ list(pass = TRUE, message = paste0("Correct: [", round(expected[1], 2), ", ", round(expected[2], 2), "]. The population mean is 73.89, so this interval does contain it - which about 19 intervals in 20 will."))
} else if (isTRUE(all.equal(value, sort(m + c(-1, 1) * 1.96 * se), tolerance = 1e-6, check.attributes = FALSE))) {
list(pass = FALSE, message = "You used 1.96, which comes from the normal distribution and assumes you KNOW the SD. You estimated it from 50 students, so the multiplier is qt(0.975, df = 49) = 2.01 - a slightly wider interval, and that extra width is the price of not knowing sigma.")
} else if (isTRUE(all.equal(value, sort(m + c(-1, 1) * se), tolerance = 1e-6, check.attributes = FALSE))) {
diff --git a/src/content/exercises/module-08.ts b/src/content/exercises/module-08.ts
index 7142d11..06e5282 100644
--- a/src/content/exercises/module-08.ts
+++ b/src/content/exercises/module-08.ts
@@ -271,17 +271,18 @@ export const module08: ExerciseDef[] = [
} else {
# A band, not a value: power here is estimated by simulation, and every
# legitimate route draws its own random numbers. The true value for
- # n = 100 against mu = 70 is about .75, and 1000 replicates give a
- # standard error of about .013, so .67 to .85 is about six standard errors
- # either way. The wrong answers land at about .24 (the complement),
- # .05 (alpha), .06 (the mean p-value) and .12 (n = 10).
- if (value >= 0.67 && value <= 0.85) {
+ # n = 100 against mu = 70 is about .89, and 1000 replicates give a
+ # standard error of about .010, so .83 to .95 is about six standard errors
+ # either way. The wrong answers land at about .11 (the complement),
+ # .14 (n = 10), .03 (alpha) and .02 (the mean p-value). The first two are
+ # too close to tell apart by value, so they share a message.
+ if (value >= 0.83 && value <= 0.95) {
list(pass = TRUE, message = paste0("About ", round(100 * value), " studies in 100 would detect this effect. That is the power of the design - and it means roughly ", round(100 * (1 - value)), " in 100 would miss it and report a non-significant result, even though the effect is genuinely there."))
- } else if (value >= 0.15 && value <= 0.33) {
- list(pass = FALSE, message = "That is the proportion of studies that FAILED to reject - the Type II error rate. Power is its complement: count p_values below alpha, not above it.")
- } else if (value <= 0.10) {
+ } else if (value >= 0.09 && value <= 0.20) {
+ list(pass = FALSE, message = "That is far below this design's power. Two mistakes land here. You may have counted the studies that FAILED to reject, which is the Type II error rate: power is its complement, so count p_values below alpha, not above it. Or each study has far fewer than the 100 students the exercise specifies.")
+ } else if (value < 0.09) {
list(pass = FALSE, message = "That is close to alpha, the rejection rate you get when the null is TRUE. Power is the rejection rate when the null is FALSE, so the test has to be against mu = 70 - a value the population mean is genuinely not equal to. (If you averaged the p-values instead of counting rejections, that also lands here.)")
- } else if (value < 0.67) {
+ } else if (value < 0.83) {
list(pass = FALSE, message = paste0("A power of ", round(value, 2), " is too low for this design. Check the sample size inside replicate(): the exercise specifies 100 students per study, and power climbs steeply with n."))
} else {
list(pass = FALSE, message = paste0("A power of ", round(value, 2), " is higher than this design can deliver. Check that alpha is 0.05 and that each study samples 100 students."))
@@ -340,7 +341,7 @@ export const module08: ExerciseDef[] = [
} else if (abs(abs(got) - abs(target)) > 1e-6) {
list(pass = FALSE, message = paste0("d is ", round(got, 3), ", but it should be ", round(target, 3), ". Check the pooled SD: each group's variance times its n - 1, added, divided by n1 + n2 - 2, then the square root."))
} else {
- list(pass = TRUE, message = paste0("Correct: d = ", format(round(abs(target), 2), nsmall = 2), ". The whole population's d is 0.50, so this significant small study overestimates the effect, as significant small studies tend to."))
+ list(pass = TRUE, message = paste0("Correct: d = ", format(round(abs(target), 2), nsmall = 2), ". The whole population's d is 0.47, so this significant small study overestimates the effect, as significant small studies tend to."))
}
}
`,
diff --git a/src/content/lessons/05-1-density-and-area.mdx b/src/content/lessons/05-1-density-and-area.mdx
index 5e284b6..218afff 100644
--- a/src/content/lessons/05-1-density-and-area.mdx
+++ b/src/content/lessons/05-1-density-and-area.mdx
@@ -12,9 +12,9 @@ population <- read.csv("data/wellbeing-population.csv", stringsAsFactors = TRUE)
population %>% summarise(mu = mean(exam_score), sigma = sd(exam_score), n = n())`} />
-Two numbers: a mean of about 73.3 and a standard deviation of about 12.4. (sd()
-divides by n − 1; the textbook's population σ divides by N and gives 12.35
-instead of 12.36, a difference that changes nothing in this module.) The
+Two numbers: a mean of about 73.9 and a standard deviation of about 12.1. (sd()
+divides by n − 1; the textbook's population σ divides by N and gives 12.122
+instead of 12.124, a difference that changes nothing in this module.) The
claim of this lesson is that those two numbers are almost the whole story.
@@ -80,13 +80,13 @@ pnorm(85, mean = mu, sd = sigma) - pnorm(65, mean = mu, sd = sigma)
# And the model can be checked against the population it describes.
mean(population$exam_score < 60)`} />
-Compare the first line with the last. The model says about 14 per cent of students score
-below 60; the population itself says about 15 per cent. Close, not identical —
+Compare the first line with the last. The model says about 12.6 per cent of students score
+below 60; the population itself says 13.3 per cent. Close, not identical —
which is what "the data are approximately normal" means in practice.
Notice also what the area of a single point must be. A point has no width, so
-`pnorm(73.3, mu, sigma) - pnorm(73.3, mu, sigma)` is exactly zero: the probability of scoring
-*exactly* 73.3 is zero under a continuous model. That is not a paradox. It is
+`pnorm(73.9, mu, sigma) - pnorm(73.9, mu, sigma)` is exactly zero: the probability of scoring
+*exactly* 73.9 is zero under a continuous model. That is not a paradox. It is
the price of modelling a score as a real number rather than as a count.
## See it move
@@ -114,9 +114,9 @@ at 1 however wide the curve spreads.
id="i-5-1"
question="You are writing up the distribution of exam scores for a methods report. Which sentence reports what you have actually computed?"
choices={[
- { text: 'Exam scores were approximately normally distributed (μ = 73.31, σ = 12.36). Under this model, 14% of students are expected to score below 60.', correct: true, response: 'Correct. It names the model, gives the two parameters in APA form, and reports the tail area as an expected proportion rather than as a claim about any one student.' },
- { text: 'The density of exam scores at 60 was .018, so 1.8% of students scored 60.', response: 'That is dnorm(60), a height. Heights are not probabilities, and no student scores exactly 60 under a continuous model.' },
- { text: 'The probability that a student scored exactly 60 was .14.', response: '.14 is the area to the LEFT of 60, covering every score below it. The probability of any exact score under a continuous model is zero.' },
- { text: 'Exam scores were normally distributed (μ = 73.31, σ = 12.36), so 14% of students scored below 60.', response: 'Two problems. "Were normally distributed" overstates it (the fit is close, not exact), and the 14% is what the model expects, while the population itself holds about 15%.' },
+ { text: 'Exam scores were approximately normally distributed (μ = 73.89, σ = 12.12). Under this model, 13% of students are expected to score below 60.', correct: true, response: 'Correct. It names the model, gives the two parameters in APA form, and reports the tail area as an expected proportion rather than as a claim about any one student.' },
+ { text: 'The density of exam scores at 60 was .017, so 1.7% of students scored 60.', response: 'That is dnorm(60), a height. Heights are not probabilities, and no student scores exactly 60 under a continuous model.' },
+ { text: 'The probability that a student scored exactly 60 was .13.', response: '.13 is the area to the LEFT of 60, covering every score below it. The probability of any exact score under a continuous model is zero.' },
+ { text: 'Exam scores were normally distributed (μ = 73.89, σ = 12.12), so 13% of students scored below 60.', response: 'Two problems. "Were normally distributed" overstates it (the fit is close, not exact), and the 13% is what the model expects (12.6%), while the population itself holds 13.3%.' },
]}
/>
diff --git a/src/content/lessons/05-2-z-scores.mdx b/src/content/lessons/05-2-z-scores.mdx
index f8e03ad..4136368 100644
--- a/src/content/lessons/05-2-z-scores.mdx
+++ b/src/content/lessons/05-2-z-scores.mdx
@@ -21,7 +21,7 @@ population %>%
-An exam score of 85 is 0.95 SDs above the mean. Sleeping 9.1 hours is 2.00 SDs
+An exam score of 85 is 0.92 SDs above the mean. Sleeping 9.1 hours is 1.99 SDs
above the mean. The sleeper is the more unusual of the two, and no amount of staring at "85" and
"9.1" would have told you that.
@@ -94,7 +94,7 @@ about two standard errors of the population mean" becomes the confidence interva
id="q-z"
question="A student's exam score has z = −1.5. Which statement is correct?"
choices={[
- { text: 'They scored 1.5 points below the mean', response: 'A z-score is not in the original units. −1.5 means 1.5 standard deviations, which here is about 18.5 exam points.' },
+ { text: 'They scored 1.5 points below the mean', response: 'A z-score is not in the original units. −1.5 means 1.5 standard deviations, which here is about 18.2 exam points.' },
{ text: 'They scored 1.5 standard deviations below the mean, placing them in roughly the bottom 7% of students', correct: true, response: 'Right: pnorm(-1.5) is .067, so about 7 students in 100 score below them.' },
{ text: 'They scored better than 1.5% of students', response: 'The −1.5 is a distance in SDs, not a percentage. Feed it to pnorm() to get a percentage.' },
{ text: 'Their score is invalid, because z-scores cannot be negative', response: 'Half of all z-scores are negative — every value below the mean has one.' },
@@ -107,9 +107,9 @@ about two standard errors of the population mean" becomes the confidence interva
id="i-5-2"
question="A colleague asks you to describe, in a sentence fit for a report, the student who scored 85. Which one is right?"
choices={[
- { text: 'The student scored 0.95 standard deviations above the population mean (μ = 73.31, σ = 12.36, z = 0.95), placing them at approximately the 83rd percentile.', correct: true, response: 'Correct. It gives the parameters the z was computed from and converts the z into a percentile, which is what a reader actually wants.' },
- { text: 'The student scored better than 95% of their peers (z = 0.95).', response: 'The 0.95 is a distance in standard deviations, not a percentile. pnorm(0.95) = .83, so the figure is 83%, not 95%.' },
- { text: 'The student scored 95% of the population mean (z = 0.95).', response: 'A z-score is not a ratio to the mean. It is a count of standard deviations away from it.' },
- { text: 'The student score was significant (z = 0.95, p < .05).', response: 'Nothing has been tested. A z-score describes where one value sits in a distribution; it is not a hypothesis test, and 0.95 would not be significant in any case.' },
+ { text: 'The student scored 0.92 standard deviations above the population mean (μ = 73.89, σ = 12.12, z = 0.92), placing them at approximately the 82nd percentile.', correct: true, response: 'Correct. It gives the parameters the z was computed from and converts the z into a percentile, which is what a reader actually wants.' },
+ { text: 'The student scored better than 92% of their peers (z = 0.92).', response: 'The 0.92 is a distance in standard deviations, not a percentile. pnorm(0.92) = .82, so the figure is 82%, not 92%.' },
+ { text: 'The student scored 92% of the population mean (z = 0.92).', response: 'A z-score is not a ratio to the mean. It is a count of standard deviations away from it.' },
+ { text: 'The student score was significant (z = 0.92, p < .05).', response: 'Nothing has been tested. A z-score describes where one value sits in a distribution; it is not a hypothesis test, and 0.92 would not be significant in any case.' },
]}
/>
diff --git a/src/content/lessons/05-3-probabilities.mdx b/src/content/lessons/05-3-probabilities.mdx
index 5cc8d70..e3dabdd 100644
--- a/src/content/lessons/05-3-probabilities.mdx
+++ b/src/content/lessons/05-3-probabilities.mdx
@@ -18,7 +18,7 @@ sigma <- sd(population$exam_score)
pnorm(85, mean = mu, sd = sigma)
# Probability in, score out.
-qnorm(0.828, mean = mu, sd = sigma)
+qnorm(0.820, mean = mu, sd = sigma)
# Round trip: qnorm undoes pnorm.
qnorm(pnorm(85, mean = mu, sd = sigma), mean = mu, sd = sigma)`} />
@@ -41,7 +41,7 @@ qnorm(0.10, mean = mu, sd = sigma, lower.tail = FALSE)
# Check it against the population the model describes.
mean(population$exam_score > qnorm(0.90, mean = mu, sd = sigma))`} />
-The model puts the distinction cut-off at 89.1, and 504 of the actual 5000
+The model puts the distinction cut-off at 89.4, and 509 of the actual 5000
students, just over 10 per cent, clear it. Two numbers, a mean and an SD, were enough
to answer a question nobody had asked when the data were collected.
@@ -92,9 +92,9 @@ the cut with 0.025 to its left sits at about −1.96.
id="i-5-3"
question="The exam board asks you to justify a distinction cut-off of 89. Which sentence reports the calculation honestly?"
choices={[
- { text: 'Modelling exam scores as normal (μ = 73.31, σ = 12.36), the 90th percentile falls at 89.14; 10% of students would be expected to score above that cut-off.', correct: true, response: 'Correct. It names the model and its parameters, gives the quantile, and states the consequence as an expectation rather than a certainty.' },
- { text: 'The top 10% of students scored 89.14.', response: 'A cut-off is not a group, and 89.14 is not anyone’s score. It is the boundary above which the top decile falls.' },
+ { text: 'Modelling exam scores as normal (μ = 73.89, σ = 12.12), the 90th percentile falls at 89.43; 10% of students would be expected to score above that cut-off.', correct: true, response: 'Correct. It names the model and its parameters, gives the quantile, and states the consequence as an expectation rather than a certainty.' },
+ { text: 'The top 10% of students scored 89.43.', response: 'A cut-off is not a group, and 89.43 is not anyone’s score. It is the boundary above which the top decile falls.' },
{ text: 'The probability of scoring above 89 was 1.28.', response: '1.28 is qnorm(0.90) on the standard normal — a z-score. Probabilities cannot exceed 1.' },
- { text: 'Exactly 500 of the 5000 students scored above 89.14, because 10% of 5000 is 500.', response: 'That is what the model predicts, not what the data did. Counting the actual population gives a number close to 500 but not equal to it.' },
+ { text: 'Exactly 500 of the 5000 students scored above 89.43, because 10% of 5000 is 500.', response: 'That is what the model predicts, not what the data did. Counting the actual population gives a number close to 500 but not equal to it.' },
]}
/>
diff --git a/src/content/lessons/07-1-standard-error-to-interval.mdx b/src/content/lessons/07-1-standard-error-to-interval.mdx
index 4a082ff..8c7d5f4 100644
--- a/src/content/lessons/07-1-standard-error-to-interval.mdx
+++ b/src/content/lessons/07-1-standard-error-to-interval.mdx
@@ -98,11 +98,11 @@ t.test(study$exam_score)$conf.int`} />
diff --git a/src/content/lessons/07-2-what-95-percent-means.mdx b/src/content/lessons/07-2-what-95-percent-means.mdx
index 5f76d33..3cc1024 100644
--- a/src/content/lessons/07-2-what-95-percent-means.mdx
+++ b/src/content/lessons/07-2-what-95-percent-means.mdx
@@ -1,7 +1,7 @@
Here is a sentence that appears in published papers, in textbooks, and in about
nine out of ten student reports:
-> *"We are 95% confident that the true mean lies between 69.1 and 75.8, so
+> *"We are 95% confident that the true mean lies between 70.3 and 77.0, so
> there is a 95% chance it is in that range."*
The first half is standard usage. The second half is wrong, and this lesson is
@@ -41,7 +41,7 @@ intervals$captured <- intervals$lower <= mu & intervals$upper >= mu
sum(intervals$captured)`} />
-With this seed, 90 of the hundred contain μ and 10 do not. That is more misses
+With this seed, 91 of the hundred contain μ and 9 do not. That is more misses
than the five you would expect, which is itself sampling variation; over many
runs the capture rate settles at 95 per cent. Now look at them.
@@ -87,12 +87,12 @@ the sampling distribution being close to normal.
Three sentences, ranked:
-1. **"95% CI [69.1, 75.8]."** Always safe. Report the interval and let it speak.
-2. **"We are 95% confident the population mean lies in [69.1, 75.8]."**
+1. **"95% CI [70.3, 77.0]."** Always safe. Report the interval and let it speak.
+2. **"We are 95% confident the population mean lies in [70.3, 77.0]."**
Standard usage. "Confident" is a term of art here meaning "produced by a
procedure with 95 per cent coverage", and every reader in the field takes it
that way.
-3. **"There is a 95% chance the population mean lies in [69.1, 75.8]."** Wrong.
+3. **"There is a 95% chance the population mean lies in [70.3, 77.0]."** Wrong.
It puts the randomness in the parameter, which does not vary, instead of in
the interval, which does.
@@ -116,9 +116,9 @@ at all.
id="i-7-2"
question="A colleague asks you to explain, in your report, what the confidence interval means. Which sentence goes in?"
choices={[
- { text: 'Mean exam score was 72.4, 95% CI [69.1, 75.8]. Intervals constructed this way contain the population mean in 95% of repeated samples.', correct: true, response: 'Correct, and this is the form a careful reader is looking for: the coverage is attributed to the construction, across repeated samples.' },
+ { text: 'Mean exam score was 73.6, 95% CI [70.3, 77.0]. Intervals constructed this way contain the population mean in 95% of repeated samples.', correct: true, response: 'Correct, and this is the form a careful reader is looking for: the coverage is attributed to the construction, across repeated samples.' },
{ text: 'There is a 95% chance that the true mean is in this interval.', response: 'The classic misstatement. The true mean is fixed; this interval is fixed once computed. The 95% describes the procedure over repeated samples, not this one result.' },
- { text: '95% of our sample scored between 69.1 and 75.8.', response: 'That describes students, and would need the SD. The interval describes the precision of the mean.' },
+ { text: '95% of our sample scored between 70.3 and 77.0.', response: 'That describes students, and would need the SD. The interval describes the precision of the mean.' },
{ text: 'We can be 95% certain that a replication would produce a mean inside this interval.', response: 'A prediction interval for a future study mean is a different and wider interval. A confidence interval is about the parameter, not about the next sample.' },
]}
/>
diff --git a/src/content/lessons/07-3-error-bars.mdx b/src/content/lessons/07-3-error-bars.mdx
index fb10ecf..0eab476 100644
--- a/src/content/lessons/07-3-error-bars.mdx
+++ b/src/content/lessons/07-3-error-bars.mdx
@@ -22,7 +22,7 @@ Three columns, three lengths, one dataset:
- **`sd_exam`**: how much students differ from each other. About 10 to 12 points.
- **`se`**: how much the group mean would differ from study to study. About
- 1.3 to 1.6 points, because it is the SD divided by the square root of the
+ 1.2 to 1.6 points, because it is the SD divided by the square root of the
group size (about 60).
- **`ci`**: the half-width of the 95 per cent interval: the standard error
times `qt(0.975, df = n - 1)`, so a shade over twice the SE.
@@ -97,11 +97,11 @@ and Module 8 computes it.
diff --git a/src/content/lessons/08-1-null-distribution.mdx b/src/content/lessons/08-1-null-distribution.mdx
index 215c65f..82723ef 100644
--- a/src/content/lessons/08-1-null-distribution.mdx
+++ b/src/content/lessons/08-1-null-distribution.mdx
@@ -1,5 +1,5 @@
A study finds that students who sleep seven hours or more score higher on the
-exam than students who sleep less. The gap is about seven points. Before anyone
+exam than students who sleep less. The gap is about six and a half points. Before anyone
can say whether that means anything, one question has to be answered:
> **How big a gap would this study have produced if sleep made no difference at
@@ -106,9 +106,9 @@ testing is looking at that picture and asking how surprising the dashed line is.
id="i-8-1"
question="How should the null distribution you just built be described in a results section?"
choices={[
- { text: 'Students sleeping seven hours or more scored higher (M = 73.0) than those sleeping less (M = 65.9). In 2000 random reallocations of the sleep labels, 1.4% of reallocations produced a difference at least this large in absolute value.', correct: true, response: 'Correct. It reports the observed means, names the procedure and the number of reallocations, and states the tail proportion as a property of the reallocations - not as a probability about the hypothesis.' },
+ { text: 'Students sleeping seven hours or more scored higher (M = 73.0) than those sleeping less (M = 66.5). In 2000 random reallocations of the sleep labels, 3.6% of reallocations produced a difference at least this large in absolute value.', correct: true, response: 'Correct. It reports the observed means, names the procedure and the number of reallocations, and states the tail proportion as a property of the reallocations - not as a probability about the hypothesis.' },
{ text: 'The null distribution shows that the observed difference was due to chance.', response: 'The null distribution shows what chance ALONE would produce. The observed difference sitting in its tail is evidence against that account, not for it.' },
- { text: 'The null distribution of exam scores was approximately normal, centred on zero.', response: 'Exam scores centre on 73, not on zero. What centres on zero is the distribution of the DIFFERENCE between two group means under the null.' },
+ { text: 'The null distribution of exam scores was approximately normal, centred on zero.', response: 'Exam scores centre on 74, not on zero. What centres on zero is the distribution of the DIFFERENCE between two group means under the null.' },
{ text: 'Because the observed difference fell in the tail of the null distribution, the null hypothesis is false.', response: 'Falls in the tail means "would be unusual if the null were true". Unusual things happen; one study in twenty produces a tail result with no effect present at all.' },
]}
/>
diff --git a/src/content/lessons/08-2-p-values-and-alpha.mdx b/src/content/lessons/08-2-p-values-and-alpha.mdx
index fb7eee1..558978c 100644
--- a/src/content/lessons/08-2-p-values-and-alpha.mdx
+++ b/src/content/lessons/08-2-p-values-and-alpha.mdx
@@ -118,11 +118,11 @@ neither can a reader.
diff --git a/src/content/lessons/08-3-errors-and-power.mdx b/src/content/lessons/08-3-errors-and-power.mdx
index 19b9aa6..8b876f2 100644
--- a/src/content/lessons/08-3-errors-and-power.mdx
+++ b/src/content/lessons/08-3-errors-and-power.mdx
@@ -40,10 +40,10 @@ kind you are holding.
@@ -56,7 +56,7 @@ p_values <- replicate(1000, {
mean(p_values < 0.05)`} />
-Roughly three quarters. Which means roughly a quarter of these studies —
+Roughly nine in ten. Which means roughly one in ten of these studies —
correctly run, correctly analysed, with a genuine effect present — report
nothing. Had one of them been your own analysis, you would have concluded there was no
effect, and you would have been wrong.
@@ -86,7 +86,7 @@ curve_data %>%
theme_classic()`} />
- **Sample size.** The one you control. Power climbs steeply and then flattens;
- the conventional target of .80 needs about 110 students here.
+ the conventional target of .80 needs about 80 students here.
- **Effect size.** Set by the world. A bigger gap is easier to see, and this one
is modest.
- **α.** Lowering it to .01 to be safer about false positives lowers power at
diff --git a/src/content/lessons/08-4-effect-sizes-and-planning.mdx b/src/content/lessons/08-4-effect-sizes-and-planning.mdx
index 9be9b78..5ec0627 100644
--- a/src/content/lessons/08-4-effect-sizes-and-planning.mdx
+++ b/src/content/lessons/08-4-effect-sizes-and-planning.mdx
@@ -14,7 +14,7 @@ b <- study$exam_score[study$sleep_group == "under 7"]
mean(a) - mean(b)`} />
This is the study of 60 students from Lessons 8-1 and 8-2. Students who sleep seven hours
-or more scored about 7 points higher. Is 7 points a lot? That depends on how
+or more scored about 6.4 points higher. Is 6.4 points a lot? That depends on how
much exam scores vary, and a raw difference does not say.
## Cohen's d
@@ -48,13 +48,13 @@ pooled <- sqrt(((length(pa) - 1) * var(pa) + (length(pb) - 1) * var(pb)) /
(mean(pa) - mean(pb)) / pooled`} />
-The true d is 0.50. The study found 0.64, and it was significant.
+The true d is 0.47. The study found 0.57, and it was significant.