SOLUTION: A sample of 12 measurements has a mean of 31 and a standard deviation of 4.75. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements havi

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Question 1193598: A sample of 12 measurements has a mean of 31 and a standard deviation of 4.75. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements having a common value of 31 each.
Find the standard deviation of the sample of 14 measurements.
Answer by Boreal(15235) (Show Source):
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the variance is the sum of the squared deviations divided by (n-1)
so sd is sqrt(SSD/n-1)=4.75
and 22.5625(n-1)=SSD=22.5625*11=248.1875
There is the same sum of squared deviations with two more values added that are exactly 31, so now the variance is 248.1875/13=19.09
that makes the sd=4.37
this is essentially multiplying the original sd by the ratio of the sqrt of the old sample size-1/new one-1, since sd is proportional to the inverse square of n-1 for samples. 4.75*sqrt(11)/sqrt(13)=4.37