# two series X and Y , 50 items each, have standard deviation 4.5 and 3.5 respectively.if the sumission of the product of deviations of X and Y series from their respective arithmetic mean is 420 , find the coefficient of corelation between X and Y.

Given, N= 50

${\sigma}_{x}=4.5\phantom{\rule{0ex}{0ex}}{\sigma}_{y}=3.5$

∑xy = 420

$r=\frac{\sum xy}{N{\sigma}_{x}{\sigma}_{y}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}r=\frac{420}{50\times 4.5\times 3.5}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}r=\frac{420}{787.5}\phantom{\rule{0ex}{0ex}}r=0.533$

Coefficient of correlation = 0.533

Regards

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