If the mode of the following data is 125, then what is the value of x?

Class	110-115	115-120	120-125	125-130	130-135
Frequency	13	31	39	x	15

Correct option is D

Given:

The mode of the data is 125, and the frequencies for the classes are provided. We need to find the value of x

Concept Used:

To calculate the mode of a grouped frequency distribution, the formula is:

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

Where:

L is the lower boundary of the modal class

$$f_1$$​ is the frequency of the modal class

$$f_0$$​ is the frequency of the class before the modal class

$$f_2$$​ is the frequency of the class after the modal class

h is the class width 

Solution: 

$$125 = 120 + \frac{(39 - 31)}{(2(39) - 31 - x)} \times 5 \\\ \\125 = 120 + \frac{8}{(78 - 31 - x)} \times 5\\\ \\125 = 120 + \frac{8}{(47 - x)} \times 5\\\ \\125 - 120 = \frac{8 \times 5}{(47 - x)}\\\ \\5 = \frac{40}{(47 - x)}\\\ \\5 \times (47 - x) = 40\\\ \\235 - 5x = 40\\\ \\235 - 40 = 5x\\\ \\195 = 5x\\\ \\x = \frac{195}{5}\\\ \\x = 39$$​​
Thus, the value of x is 39.