Find the mode for the following distribution.

Class Interval:	1-5	6-10	11-15	16-20	21-25
Frequency:	4	7	10	8	6

The modal group is then determined by finding the class with the greatest frequency.

Use the formula, ${\mathrm{m}}_{\mathrm{e}}=\mathrm{L}+\frac{{\mathrm{f}}_{\mathrm{m}}-{\mathrm{f}}_{\mathrm{m}-1}}{\left({\mathrm{f}}_{\mathrm{m}}-{\mathrm{f}}_{\mathrm{m}-1}\right)+\left({\mathrm{f}}_{\mathrm{m}}-{\mathrm{f}}_{\mathrm{m}+1}\right)}\times \mathrm{I}$

 Modal group $=11-15$, since it has the highest frequency i.e 10.

 Estimated Mode, $\mathrm{M}=\mathrm{L}+\frac{{\mathrm{f}}_{\mathrm{m}}-{\mathrm{f}}_{\mathrm{m}-1}}{{\mathrm{f}}_{\mathrm{m}}-{\mathrm{f}}_{\mathrm{m}-1}+{\mathrm{f}}_{\mathrm{m}}-{\mathrm{f}}_{\mathrm{m}+1}}\times \mathrm{w}$

The lower class boundary of the modal group, L = 10.5

Frequency of group before the modal group,  ${\mathrm{f}}_{\mathrm{m}-1}=7$

Frequency of Modal group,  ${\mathrm{f}}_{\mathrm{m}}=10$

Frequency of group after the modal group,  ${\mathrm{f}}_{\mathrm{m}+1}=8$

Group width,  $\mathrm{w}=5$

$\therefore \mathrm{M}=10.5+\frac{10-7}{10-7+10-8}\times 5$

$=10.5+\frac{3}{5}\times 5$

$=13.5$