Find the mode of the given frequency distribution.

x	0-10	10-20	20-30	30-40	40-50
f	5	8	10	2	5

Correct option is C

Given:

Formula Used:

Mode = L + $$\frac{(f_1-f_0)}{(2f_1-f_0-f_2)}\times h$$

L = Lower boundary of the modal class 

​$$f_1$$ = Frequency of the modal class

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

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

​$$h$$ = Class width

Solution:

L = 20(Lower boundary of the modal class 20-30)

​​$$f_1$$ =10 (Frequency of the modal class)

$$f_0$$ =8 (Frequency of the class preceding the modal class)

$$f_2$$ =2(Frequency of the class succeeding the modal class)

​$$h$$ =10(Class width)

Mode = 20+$$\frac{(10-8)}{(2\times10-8-2)}\times 10$$

Mode = 20 + $$\frac{2}{(20-8-2)}\times 10$$

Mode = 20 + $$\frac{2}{10}\times 10$$

Mode = 20+2 

Mode = 22

The mode of the given frequency distribution is 22.

Thus, correct option is (c)