Question

Find the mode of the following frequency distribution: [CBSE 2014]

Marks	10−20	20−30	30−40	40−50	50−60
Frequency	12	35	45	25	13

Answer 1

Here the maximum class frequency is 45, and the class corresponding to this frequency is 30−40. So, the modal class is 30−40.

Now,

modal class = 30−40, lower limit (l) of modal class = 30, class size (h) = 10,

frequency (f₁) of the modal class = 45,

frequency (f₀) of class preceding the modal class = 35,

frequency (f₂) of class succeeding the modal class = 25

Now, let us substitute these values in the formula:

$$\begin{gathered} \mathrm{Mode}=l+\left(\frac{f_1-f_0}{2f_1-f_0-f_2}\right)\times h \\ =30+\left(\frac{45-35}{90-35-25}\right)\times 10 \\ =30+\left(\frac{10}{30}\right)\times 10 \\ =30+3.33 \\ =33.33 \end{gathered}$$

Hence, the mode is 33.33.