A survey of 40 households in a neighbourhood conducted by a group of students yielded the following frequency table for the number of family members in a household -

Determine the mode of this data:

Family size	1-3	3-5	5-7	7-9	9-11
No. of families	14	16	4	4	2

The modal group is then determined by finding the family size with the greatest number of families. 

Use the formula, $\text{ Mode }=\mathrm{l}+\left(\frac{{\mathrm{f}}_1-{\mathrm{f}}_0}{2{\mathrm{f}}_1-{\mathrm{f}}_0-{\mathrm{f}}_2}\right)\times \mathrm{h}$

Here the maximum class frequency is 16, and the class corresponding to this frequency is $3-5$. So, the modal class is $3-5$.

Now, in the modal class $3-5$, the lower limit of the modal class is $\mathrm{l}=3$, 

class size, $\left(\mathrm{h}\right)=2$, 

frequency of the modal class, $\left({\mathrm{f}}_1\right)=16$, 

frequency of class preceding the modal class, $\left({\mathrm{f}}_0\right)=14$, 

frequency of class succeeding the modal class, $\left({\mathrm{f}}_2\right)=4$,

Substituting these values in the formula, we have

$\text{ Mode }=\mathrm{l}+\left(\frac{{\mathrm{f}}_1-{\mathrm{f}}_0}{2{\mathrm{f}}_1-{\mathrm{f}}_0-{\mathrm{f}}_2}\right)\times \mathrm{h}$

$=3+\left(\frac{16-14}{2\times 16-14-4}\right)\times 2$

$=3+\left(\frac{2}{14}\right)\times 2$

$=3+\frac{4}{14}$

$=3.29$