From the following information, determine coefficient of correlation between X and Y series:

X-Series Y-Series

Number of Items 15 15

Mean 25 18

SD 3.01 3.03

Sum of Squares of deviation from Mean 136 138

Sum of product of deviation of X and Y from their respective Means 122

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Solution

$G i v e n : N = 15 X = 25 Y = 18 σ_{x} = 3.01 σ_{y} = 3.03 Σ x^{2} = 136 Σ y^{2} = 138 Σ x y = 122 r = \frac{Σ x y}{N σ_{x} σ_{y}} = \frac{122}{15 \times 3.01 \times 3.03} = 0.89$
Hence, coefficient of correlation between X and Y series is + 0.89

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	X-Series	Y-Series
Mean	80	120
Sum of Squares of deviation from Arithmetic Mean	56	156
Sum of product of deviation of X and Y from their respective Means	92

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Arithmetic Mean	25	18
Sum of Square of deviations from Arithmetic Mean	136	138

Compute coefficient of correlation from the following data:

Sum of products of deviations of X and Y series from their respective mean is 20. Number of pairs of observations is 10.

X	+5	−4	−2	+20	−10	0	+3	0	−15	−5
Y	+5	−12	−7	+25	−10	−3	0	+2	−9	−15

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	X-Series	Y-Series
Number of Items	15	15
Mean	25	18
SD	3.01	3.03
Sum of Squares of deviation from Mean	136	138
Sum of product of deviation of X and Y from their respective Means	122