Question

Question 6 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?

Class X1 - Maths -Statistics Page 380

Answer 1

Here, total number of observation ( n ) = 50
For Mathematics,
$coefficient\:of\: variation(CV)=\frac{\sigma}{\overline{x}}\times\:100\\\\here,\sigma=12,\overline{x}=42\\\\so,\\CV=\frac{12}{42}\times\:100\\\\=\frac{200}{7}=28.57$
For physics,
$coefficient\:of\: variation(CV)=\frac{\sigma}{\overline{x}}\times\:100\\\\here,\sigma=15,\overline{x}=32\\\\so,\\CV=\frac{15}{32}\times\:100\\\\=\frac{1500}{32}=46.87$
For chemistry,
$coefficient\:of\: variation(CV)=\frac{\sigma}{\overline{x}}\times\:100\\\\here,\sigma=20,\overline{x}=40.9\\\\so,\\CV=\frac{20}{40.9}\times\:100\\\\=\frac{2000}{40.9}=48.89$
hence,
from above we observed that ,
CV of chemistry > CV of physics > CV of mathematics
so, chemistry shows highest variability and mathematics shows lowest variability.