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Question
Calculate the coefficient of correlation between X and Y series from the following data.
| Description | X | Y |
| Number of pairs of observation | 15 | 15 |
| Arithmetic mean | 25 | 18 |
| Standard deviation | 3.01 | 3.03 |
| Sum of squares of deviation from the arithmetic mean | 136 | 138 |
Summation of product deviations of X and Y series from their respective arithmetic means is 122.
Solution
N = 15, `bar"X"` = 25, `bar"Y"` = 18, ∑X2 = 138, ∑Y2 = 138, ∑XY = 122
Correlation coefficient
r = `(sum"XY")/(sqrt(sum"X"^2 sum "y"^2))`
= `122/(sqrt (136 xx 138))`
= `122/136.996`
= 0.891
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