Standard Deviation of sample

Probability Level 2

The standard deviation of a sample of 20 observations is 3 , if each of these observations is multiplied by 3 what is the standard deviation of the resulting set of observations ?


The answer is 9.

Srinivasa Gopal by Srinivasa Gopal , 53, India

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1 solution

By definition, standard deviation of a given number of statistices is < x 2 > − ( < x > ) 2 \sqrt {<x^2>-(<x>)^2} . When each statistic is multiplied n n times, the S.D. becomes < ( n x ) 2 > − ( < n x > ) 2 = n × < x 2 > − ( < x > ) 2 \sqrt {<(nx)^2>-(<nx>)^2}=n\times \sqrt {<x^2>-(<x>)^2} . In this case, the original S.D. is 3 3 and n = 3 n=3 . So the new S.D. will be 3 × 3 = 9 3\times 3=\boxed 9

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