Question

The mode of the following frequency distribution is

Class Interval	Frquency
0-10	5
10-20	10
20-30	8
30-40	13
40-50	12

• A. $\frac{115}{3}$
• B. 40
• C. $\frac{98}{3}$
• D. 34

Answer 1

The correct option is A $\frac{115}{3}$

Here, the class interval 30 - 40 has the highest frequency 13.
Thus, the modal class is 30 - 40.
Here,
Lower limit of modal class (l) = 30
Class size (h) = 40 – 30 = 10
Frequency of the modal class $\left(f_1\right)$ = 13
Frequency of the class preceding to the modal class $\left(f_0\right)$ = 8
Frequency of the class succeeding to the modal class $\left(f_2\right)$ = 12
$\therefore Mode=l+\frac{f_1-f_0}{2f_1-f_0-f_2}\times h$
$Mode=30+\left[\frac{13-8}{(2\times 13)-8-12}\right]\times 10$
$=30+\frac{50}{6}$
$=\frac{180+50}{6}=\frac{230}{6}=\frac{115}{3}$
Hence, the correct answer is option a.