Question

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

$$\begin{array}{cccccc}Ageoffamilymember& 0-20& 20-40& 40-60& 60-80& 80-100\\ Numberofstudents& 7& 8& 2& 2& 1\end{array}$$

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

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

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

$=22.85$