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A sample of 20 observations has a standard deviation of 4. the sum of the squared deviations from the sample mean is:

User Isolin
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3 votes

Answer: 304.

Explanation:

The formula to calculate the sample standard deviation is given by :-


s=\sqrt{\frac{\sum(x-\overline{x})^2}{n-1}}

, where x = sample element.


\overline{x} = Sample mean

s=sample standard deviation.

n= Number of observations.


\sum(x-\overline{x})^2 = sum of the squared deviations from the sample mean

As per given , we have

s=4

n= 20

Substitute theses values in the above formula , we get


4=\sqrt{\frac{\sum(x-\overline{x})^2}{20-1}}


4=\sqrt{\frac{\sum(x-\overline{x})^2}{19}}

Square root on both sides , we get


\Righatrrow\ 16=\frac{\sum(x-\overline{x})^2}{19}\\\\\Righatrrow\ \sum(x-\overline{x})^2=16*19=304

Hence, the sum of the squared deviations from the sample mean is 304.

User Uzhas
by
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