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Question
Find the coefficient of correlation for the following:
| Cost (₹) | 14 | 19 | 24 | 21 | 26 | 22 | 15 | 20 | 19 |
| Sales (₹) | 31 | 36 | 48 | 37 | 50 | 45 | 33 | 41 | 39 |
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Solution
| X | Y | x = `"X" - bar"X"` = X − 20 |
y = `"Y" - bar"Y"` = Y − 40 |
x2 | y2 | xy |
| 14 | 31 | − 6 | − 9 | 36 | 81 | 54 |
| 19 | 36 | − 1 | − 4 | 1 | 16 | 4 |
| 24 | 48 | 4 | 8 | 16 | 64 | 32 |
| 21 | 37 | 1 | − 3 | 1 | 9 | − 3 |
| 26 | 50 | 6 | 10 | 36 | 100 | 60 |
| 22 | 45 | 2 | 5 | 4 | 25 | 10 |
| 15 | 33 | − 5 | − 7 | 25 | 49 | 35 |
| 20 | 41 | 0 | 1 | 0 | 1 | 0 |
| 19 | 39 | − 1 | − 1 | 1 | 1 | 1 |
| 180 | 360 | 0 | 0 | 120 | 346 | 193 |
N = 9, ∑X = 180, ∑Y = 360, ∑x2 = 120, ∑y2 = 346, ∑xy = 193, `bar"X" = (sum"X")/"N" = 180/9` = 20, `bar"Y" = (sum"Y")/"N" = 360/9` = 40.
Correlation coefficient (r) = `(sum"xy")/(sqrt(sum"x"^2 sum"y"^2))`
r = `193/sqrt (120 xx 346)`
r = 0.947
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