Question 7 (a)
Find the coefficient of correlation between age and playing habits of the following students and comment on the result.
As per the Given Data
Age of Players (X):
16, 17, 18, 19, 20, 21, 22
Number of Regular Players (Y):
2250, 1700, 1260, 900, 480, 180, 60
By apply Method Used
Karl Pearson’s Coefficient of Correlation
Step 1: Calculation Table
Assumed Mean of X = 19
Assumed Mean of Y = 975
X | Y | dx = X−19 | dy = Y−975 | dx² | dy² | dx·dy |
|---|---|---|---|---|---|---|
16 | 2250 | −3 | 1275 | 9 | 1625625 | −3825 |
17 | 1700 | −2 | 725 | 4 | 525625 | −1450 |
18 | 1260 | −1 | 285 | 1 | 81225 | −285 |
19 | 900 | 0 | −75 | 0 | 5625 | 0 |
20 | 480 | 1 | −495 | 1 | 245025 | −495 |
21 | 180 | 2 | −795 | 4 | 632025 | −1590 |
22 | 60 | 3 | −915 | 9 | 837225 | −2745 |
Step 2: Totals
Σdx² = 28
Σdy² = 3,952,400
Σ(dx × dy) = −10,390
Step 3 : By Apply Karl Pearson’s Formula
r = Σ(dx × dy) / √(Σdx² × Σdy²)
r = −10,390 / √(28 × 3,952,400)
r = −10,390 / 10,520
r = −0.99 (approximately)
Answer
Coefficient of correlation (r) = −0.99