Question

A student scores the following marks in five tests : $45,54,41,57,43$. His score is not known for the sixth test. If the mean score is $48$ in the six tests, then the standard deviation of the marks in six tests is :

• A. $\frac{100}{3}$
• B. $\frac{10}{3}$
• C. $\frac{10}{\sqrt{3}}$
• D. $\frac{100}{\sqrt{3}}$

Answer 1

The correct option is C $\frac{10}{\sqrt{3}}$

Let marks in the sixth test be $x$.
Mean, $\overline{x}=48$
$\Rightarrow \frac{45+54+41+57+43+x}{6}=48$
$\Rightarrow x=48$

Standard deviation, $\sigma =\sqrt{\frac{\sum (x_i-\overline{x}{)}^2}{6}}$
$=\sqrt{\frac{(-3{)}^2+(6{)}^2+(-7{)}^2+(9{)}^2+(-5{)}^2+(0{)}^2}{6}}$
$=\sqrt{\frac{200}{6}}=\frac{10}{\sqrt{3}}$