Question

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

Answer 1

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.