If the mode of the following data is 160, then what is the value of x?

Class	145-150	150-155	155-160	160-165	165-170
Frequency	10	18	31	x	24

Correct option is B

Given:

Mode = 160

Modal class = 155 – 160

Frequencies:

$$f_1$$​ = 31 (modal class)

$$f_0$$​= 18 (preceding class)

$$f_2$$​ = x (succeeding class)

Class width h = 5

Formula Used:

For grouped data, the mode formula:

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

Solution:​

Lower boundary of modal class = 155

Using the formula; 

​$$160 = 155 + \left( \frac{31 - 18}{2(31) - 18 - x} \right) \cdot 5$$​​

​$$160 = 155 + \left( \frac{13}{62 - 18 - x} \right) \cdot 5$$​​

​$$160 - 155 = \frac{65}{44 - x}$$​​

​$$5 = \frac{65}{44 - x}$$​​

5(44 - x) = 65

220 - 5x = 65

155 = 5x

x = $$\frac{155}{5}$$​ = 31