The mean and standard deviation of marks obtained by 50 students of a class in three subjects, Mathematics, Physics and Chemistry are given below:
Which of the three subjects shows the highest variability in marks and which shows the lowest?
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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