Question

If $\sum _{i=1}^{10}(x_i-5)=20$ and $\sum _{i=1}^{10}(x_i-5{)}^2=660,$ $y=S.D.$ of $10$ items $x_1,x_2,x_3.....,x_{10}$, then $\left[y\right]$ is equal to (where $[.]$ represents the greatest integer function)

• A. $6$
• B. $7$
• C. $8$
• D. $9$

Answer 1

The correct option is B $7$

Let $X$ be random variable which takes values $x_1,x_2...x_{10}$
Then s.d of $X$ is
$y=\sigma \left(X\right)=\sqrt{E\left(X^2\right)-\left(E\right(X){)}^2}$
We know that $\sigma \left(X\right)=\sigma (X-5)=\sqrt{E\left(\right(X-5{)}^2)-(E(X-5){)}^2}=\sqrt{\frac{660}{10}-{\left(\frac{20}{10}\right)}^2}=\sqrt{62}$
So, $\left[y\right]=7$