Question

A survey was conducted on 20 families in a locality by a group of students .What will be the mode of the data?

$$\begin{array}{cccccc}\text{Age of family member}& 0-20& 20-40& 40-60& 60-80& 80-100\\ \text{Number of students}& 7& 8& 2& 2& 1\end{array}$$

• A. 21.85
• B. 22.86
• C. 23.87
• D. 24.87

Answer 1

The correct option is B

22.86

Using, Mode = $l+\frac{f_1-f_0}{{2f}_1-f_0-f_2}\times h$
where,
Maximum class frequency, $f_1=8$

The class corresponding to the frequency $=20-40$

Lower limit of the modal class, $l=20$

Frequency of class preceding the modal class, $f_0=7$

Frequency of class succeeding the modal class, $f_2=2$

$Now,Mode=20+\frac{8-7}{16-7-2}\times 20$

$Mode=20+\frac{1}{7}\times 20$

$\therefore Mode=22.86$