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?
Standard deviation of Mathematics = 12
Standard deviation of Physics =15
Standard deviation of Chemistry = 20
The coefficient of variation (C.V.) is given by \(\frac{Standard\,deviation}{Mean}×100\)
\(C.V(in\,Mathematics)=\frac{12}{42}×100=28.57\)
\(C.V(in\,Physics)=\frac{15}{32}×100=46.87\)
\(C.V(in\,Chemistry)=\frac{20}{40.9}×100=48.89\)
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.
| \(\text{Length (in mm)}\) | 70-80 | 80-90 | 90-100 | 100-110 | 110-120 | 120-130 | 130-140 |
|---|---|---|---|---|---|---|---|
| \(\text{Number of leaves}\) | 3 | 5 | 9 | 12 | 5 | 4 | 2 |