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Question

Standard deviation for n observations x1,x2xn is '5' then the standard deviation of n observations 5x1,5x2,5xn will be ___

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Solution

We have seen that if we multiply the data with any constant k, variance of data will be multiple of k2 of the old variance.
Given the standard deviation of x1,x2xn is 5
So variance will be = 25
now, if we multiply each term with '5' the variance (new) will be equal to (5)2 (old variance)
25×25=625
So, standard deviation will be 625=25

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