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 the three subjects shows the highest variability in marks and which shows the lowest?
| Subject | Mathematics,Physics,Chemistry |
| 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?
(D) The coefficient of variation $(C.V.)$ is defined as $\frac{\text{Standard deviation}}{\text{Mean}} \times 100$.
For Mathematics: $C.V. = \frac{12}{42} \times 100 \approx 28.57$.
For Physics: $C.V. = \frac{15}{32} \times 100 \approx 46.87$.
For Chemistry: $C.V. = \frac{20}{40.9} \times 100 \approx 48.90$.
$A$ higher $C.V.$ indicates greater variability.
Comparing the values,Chemistry has the highest $C.V.$ $(48.90)$ and Mathematics has the lowest $C.V.$ $(28.57)$.
Thus,Chemistry shows the highest variability and Mathematics shows the lowest variability.
For Mathematics: $C.V. = \frac{12}{42} \times 100 \approx 28.57$.
For Physics: $C.V. = \frac{15}{32} \times 100 \approx 46.87$.
For Chemistry: $C.V. = \frac{20}{40.9} \times 100 \approx 48.90$.
$A$ higher $C.V.$ indicates greater variability.
Comparing the values,Chemistry has the highest $C.V.$ $(48.90)$ and Mathematics has the lowest $C.V.$ $(28.57)$.
Thus,Chemistry shows the highest variability and Mathematics shows the lowest variability.
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