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 :

$\begin{array}{cccc}\text{Subject}& \text{Mathematics}& \text{Physics}& \text{Chemistry}\\ \text{Mean}& 42& 32& 40.9\\ \text{Standard deviation}& 12& 15& 20\end{array}$

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

Answer 1

Here, n = 50

For Mathematics,

Coefficient of variation (CV) $=\frac{\sigma }{x}\times 100$

= $\frac{12}{42}\times =\frac{2}{7}\times =\frac{200}{7}$

For Physics, CV = $=\frac{\sigma }{x}\times 100$ = $\frac{15}{32}\times 100$ ...(i)

$=\frac{1500}{32}=46.87$ ....(ii)

For Chemistry, CV = $=\frac{\sigma }{x}\times 100$ = $\frac{20}{40.9}\times 100=\frac{2000}{40.9}=48.89$ ....(iii)

From Eqs. (i), (ii) and (iii) , we have

$\because$ CV of chemistry > CV of Physics > CV of Mathematics

$\therefore$ Chemistry shows the highest variability and Mathematics shows the least variability.