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