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

Answer 1

Answer: (A)

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

Answer 2

Let x be the 6th observation
$\Rightarrow$ $45 + 54 + 41 + 57 + 43 + x = 48 \times 6 = 288$
$\Rightarrow x = 48$
variance = $= \left(\frac{\sum x_{i}^{2}}{6} - \left(\bar{x}\right)^{2}\right)$
$\Rightarrow variance = \frac{14024}{6} - \left(48\right)^{2}$
$= \frac{100}{3}$
$\Rightarrow standard\, deviation = \frac{10}{\sqrt{3}}$