A student scores the following marks in five tests : $54,45,41,43,57$. His score is not known for the sixth…
A student scores the following marks in five tests : $54,45,41,43,57$. His score is not known for the sixth test. If the mean score is 48 in six tests, then the standard deviation of marks in six tests is
$\frac{100}{\sqrt{3}}$
$\frac{10}{\sqrt{3}}$
$\frac{100}{3}$
$\frac{10}{3}$
Solution
Let students' sixth test score be $x$,
$\begin{aligned}
\therefore \quad & \text { Mean }=48 \\
& \Rightarrow \frac{54+45+41+43+57+x}{6}=48 \\
& \Rightarrow x=48
\end{aligned}$
$\begin{aligned} \therefore \quad & \text { Standard deviation } \\ & =\sqrt{\frac{1}{\mathrm{n}} \sum\left(x_{\mathrm{i}}-\bar{x}\right)^2} \\ = & \sqrt{\frac{1}{6} \times\left[\left(6^2+(-3)^2+(-7)^2+(-5)^2+(9)^2\right)\right]} \\ = & \sqrt{\frac{200}{6}} \\ = & \frac{10}{\sqrt{3}}\end{aligned}$