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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 :
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Verified Answer
The correct answer is:
2
2
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
$$
\begin{gathered}
=\sqrt{\frac{(6-7)^2+(7-7)^2+(8-7)^2+(10-7)^2+(4-7)^2}{5}} \\
=\sqrt{\frac{1^2+0^2+1^2+3^2+3^2}{5}}=\sqrt{\frac{20}{5}}=\sqrt{4}=2
\end{gathered}
$$
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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