Find the mean, median and mode of the following data:

Solution:

Consider the following data.

Here, the maximum frequency is 12 so the modal class is 60−80.

Therefore,

$l=60$

$h=20$

$f=12$

$f_{1}=10$

$f_{2}=6$

$F=24$

Median $=l+\frac{\frac{N}{2}-F}{f} \times h$

$=60+\frac{25-24}{12} \times 20$

$=60+\frac{1}{12} \times 20$

Median $=61.66$

Thus, the median of the data is 61.66.

Mean $=\frac{\sum f_{i} x_{i}}{\sum f}$

$=\frac{3120}{50}$

Mean = 62.4

Thus, the mean of the data is 62.4.

Mode

$=l+\frac{f-f_{1}}{2 f-f_{1}-f_{2}} \times h$

$=60+\frac{12-10}{24-10-6} \times 20$

$=60+\frac{2}{8} \times 20$

Mode $=65$

Thus, the mode of the data is 65.