Question

A student scores the following marks in five test: $45,54,41,57,43$. 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 test is

• A. $\frac{10}{\sqrt{3}}$
• B. $\frac{100}{\sqrt{3}}$
• C. $\frac{130}{3}$
• D. $\frac{10}{3}$

Answer 1

Answer: (A)

$\frac{10}{\sqrt{3}}$

Let $x$ be the $6^{th}$ observation
$\Rightarrow 45+54+41+57+43+x=48\times 6=288$
$\Rightarrow x=48$
Variance $=(\frac{\sum x_i^2}{6}-(\overline{X}{)}^2)$
$\Rightarrow$ variance $=\frac{14024}{6}-(48{)}^2$
$=\frac{100}{3}$
$\Rightarrow$ standard deviation $=\frac{10}{\sqrt{3}}$