Mean of 5 observations is 7 . If four of these observations are...

Mean of 5 observations is 7 . If four of these observations are

6,7,8,10

and one is missing then the variance of all the five observations is :

Options

Correct answer

D. 2

Step-by-step solution

Let 5 th observation be

x

. Given mean

=7

\begin{aligned}& \therefore 7=\frac{6+7+8+10+x}{5}\\ & \Rightarrow x=4 \end{aligned}

Now, Variance

\begin{gathered} =\sqrt{\frac{(6-7)^2+(7-7)^2+(8-7)^2+(10-7)^2+(4-7)^2}{5}}\\ =\sqrt{\frac{1^2+0^2+1^2+3^2+3^2}{5}}=\sqrt{\frac{20}{5}}=\sqrt{4}=2 \end{gathered}

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