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. 22.85
• C. 23.87
• D. 24.87

Answer 1

The correct option is B

22.85

Maximum class frequency ($f_1$) = 8

The class corresponding to the frequency = 20-40

Lower limit of the class (l) = 20

Frequency of class preceding the modal class = 7

Frequency of class succeeding the modal class = 2

Mode = $l+\frac{f_1-f_0}{{2f}_1-f_0-f_2}$$\times h$

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

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

$=22.85$