Question

The mean and standard deviation of marks obtained by $50$ students of a class in three subjects, Mathematics, Physics and Chemistry are given below.

Subject	Mathematics	Physics	Chemistry
Mean	$42$	$32$	$40.9$
Standard deviation	$12$	$15$	$20$

Which of these three subjects shows the highest variability in marks and which shows the lowest?

• A. Chemistry, Mathematics
• B. Mathematics, Physics
• C. Chemistry, Physics
• D. None of these

Answer 1

Answer: (A)

Here, $n = 50$
For Mathematics, $C.V.=\frac{\sigma}{\bar{x}} \times 100= \frac{12}{42}\times100=28.57\quad\ldots\left(i\right)$
For Physics, $C.V. =\frac{\sigma }{\bar{x}} \times 100= \frac{15}{32}\times 100=46.87\quad \ldots \left(ii\right)$
For Chemistry, $C.V.=\frac{\sigma }{\bar{x}} \times 100= \frac{20}{40.9}\times 100=48.89\quad \ldots \left(iii\right)$
From $\left(i\right)$, $\left(ii\right)$ and $\left(iii\right)$, we have
$C.V.$ of Chemistry $> C.V.$ of Physics $> C.V.$ of Mathematics
$\therefore $ Chemistry shows the highest variability and Mathematics shows the least variability.