A set of data presented in the form of a frequency distribution table with class intervals and their respective frequencies had a mode of 48.5. The lower boundary of the modal class was 46.5; the frequency of the modal class was 34; the frequency of the class interval just preceding the modal class was 32 and the frequency of the class interval just succeeding the modal class was 25 . What was the width of the modal class?

Correct option is D

Given:

Mode = 48.5

Lower boundary = 46.5

Frequency of modal class = 34

Frequency of preceding the modal class = 32

Frequency of succeeding the modal class = 25

Formula Used:

$$\text{Mode} = l + \frac{f_m - f_1}{2f_m - f_1 - f_2} \times h \\$$​

Where, I = Lower boundary of modal class

$$f_m$$​= Frequency of modal class

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

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

h= Class Size

Solution:

$$\text{As per the question;} \\\text{Mode} = l + \frac{f_m - f_1}{2f_m - f_1 - f_2} \times h \\\text{By putting the values,} \\48.5 = 46.5 + \frac{34 - 32}{68 - 32 - 25} \times h \\22 = 2 \times h \\h = 11$$​