Question

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?

 

Answer 1

We know: \[CV = \frac{\sigma}{\bar{X}} \times 100\]

\[\bar{{X_m}} = 42, \sigma_m = 12\]

\[ \bar{{X_p}} = 32, \sigma_p = 15\]

\[ \bar{{X_c}} = 40 . 9, \sigma_c = 20\]

CV of mathematics marks 

\[= \frac{12}{42} \times 100 = \frac{1200}{42} = 28 . 57\]

CV of physics marks ​

 

\[= \frac{15}{32} \times 100 = \frac{1500}{32} = 46 . 87\]

CV of chemistry marks  \[= \frac{20}{40 . 9} \times 100 = \frac{2000}{40 . 9} = 48 . 89\]

Since CV of chemistry is the greatest, the variability of marks in chemistry is the highest and that of mathematics is the lowest.