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

Given number of students =50
Step 1:
For mathematics, Given mean =42
Standard deviation =12
coefficient of variation $=\large\frac{\sigma}{\bar{x}}$$\times 100 \qquad= \large\frac{12}{42}$$ \times 100$
$\qquad= \large\frac{1200}{42}$
$\qquad= 28.57$
Step 2:
For physics, Given mean =32
Standard deviation =15
coefficient of variation $=\large\frac{\sigma}{\bar{x}}$$\times 100 \qquad= \large\frac{15}{32}$$ \times 100$
$\qquad= \large\frac{1500}{32}$
$\qquad= 46.87$
Step 3:
For chemistry, Given mean =40.9
Standard deviation =20
coefficient of variation $=\large\frac{\sigma}{\bar{x}}$$\times 100 \qquad= \large\frac{20}{40.9}$$ \times 100$
$\qquad= \large\frac{2000}{40.9}$
$\qquad= 48.89$
COMPARISON :
As we know that higher the coefficient of variation, higher is the variability
CV of chemistry is highest and CV of mathematics is least.
$\therefore$ Chemistry shows the highest variability and mathematics shows the least variability.