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Question

Calculate Karl Pearson's coefficient between the marks (out of 30) in English and Hindi obtained by 10 students.
Marks in English 10 25 13 25 22 11 12 25 21 20
Marks in Hindi 12 22 16 15 18 18 17 23 24 17

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Solution

Marks in English
(X)
Marks in Hindi
(Y)
X2 Y2 XY

10
25
13
25
22
11
12
25
21
20

12
22
16
15
18
18
17
23
24
17

100
625
169
625
484
121
144
625
441
400

144
484
256
225
324
324
289
529
576
289

120
550
208
375
396
198
204
575
504
340
ΣX=184 ΣY=182 ΣX2=3734 ΣY2=3440 ΣXY=3470

N = 10

r=NΣXY-ΣXΣYNΣX2-ΣX2 NΣY2-ΣY2or, r=10×3470-184×18210×3734-184210×3440-1822or, r=121259.02×35.72r=0.574

Thus, coefficient of correlation = 0.574

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