Answer: 304.
Step-by-step explanation:
The formula to calculate the sample standard deviation is given by :-
[tex]s=\sqrt{\dfrac{\sum(x-\overline{x})^2}{n-1}}[/tex]
, where x = sample element.
[tex]\overline{x}[/tex] = Sample mean
s=sample standard deviation.
n= Number of observations.
[tex]\sum(x-\overline{x})^2[/tex] = 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
[tex]4=\sqrt{\dfrac{\sum(x-\overline{x})^2}{20-1}}[/tex]
[tex]4=\sqrt{\dfrac{\sum(x-\overline{x})^2}{19}}[/tex]
Square root on both sides , we get
[tex]\Righatrrow\ 16=\dfrac{\sum(x-\overline{x})^2}{19}\\\\\Righatrrow\ \sum(x-\overline{x})^2=16\times19=304[/tex]
Hence, the sum of the squared deviations from the sample mean is 304.
