Question

Compute the mode of the following data: [CBSE 2013]

Class	0−20	20−40	40−60	60−80	80−100
Frequency	25	16	28	20	5

Answer 1

Here the maximum class frequency is 28, and the class corresponding to this frequency is 40−60. So, the modal class is 40−60.

Now,

Modal class = 40−60, lower limit (l) of modal class = 40, class size (h) = 20,

frequency (f₁) of the modal class = 28,

frequency (f₀) of class preceding the modal class = 16,

frequency (f₂) of class succeeding the modal class = 20.

Now, let us substitute these values in the formula:

$$\begin{gathered} \mathrm{Mode}=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h \\ =40+\left(\frac{28-16}{56-16-20}\right)\times 20 \\ =40+\left(\frac{12}{20}\right)\times 20 \\ =40+12 \\ =52 \end{gathered}$$

Hence, the mode is 52.