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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 | Chemistty |
| Mean | $42$ | $32$ | $40.9$ |
| Standard deviation | $12$ | $15$ | $20$ |
Which of the three subjects shows the highest variability in marks and which shows the lowest?
Solution
Standard deviation of Mathematics $=12$
Standard deviation of Physics $=15$
Standard deviation of Chemistry $=20$
The coefficient of variation $( C.V. )$ is given by $\frac{\text { Standard deviation }}{\text { Mean }} \times 100$
$C.V.$ (in Mathematics) $=\frac{12}{42} \times 100=28.57$
$C.V.$ (in Physics) $=\frac{15}{32} \times 100=46.87$
$C.V.$ (in Chemistry) $=\frac{20}{40.9} \times 100=48.89$
The subject with greater $C.V.$ is more variable than others.
Therefore, the highest variability in marks is in Chemistry and the lowest variability in marks is in Mathematics.
