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?

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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.

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