Marks	No. of students
20-30	4
30-40	16
40-50	2
50-60	7

The above data represents the number of students and the marks obtained by them. Find the mode.

The maximum frequency is 16 and 30 - 40 is the class interval that belongs to this frequency.

Therefore, the modal group is 30 - 40.

The lower limit of the modal group (l) = 30

Frequency (f₁) = 16

Size (h) = 40 - 30 = 10

Frequency of class preceding modal group (f₀) = 4

Frequency of class succeeding modal group (f₂) = 2

$$\begin{gathered} \mathrm{Mode} = \mathrm{l}+\left(\frac{{\mathrm{f}}_1-{\mathrm{f}}_0}{2{\mathrm{f}}_1-{\mathrm{f}}_0-{\mathrm{f}}_2}\right)\times \mathrm{h} \\ =30+\left(\frac{16-4}{2\times 16-4-2}\right)\times 10 \\ =30+\left(\frac{12}{26}\right)\times 10 \\ =30+(0.461)\times 10 \\ =34.61 \end{gathered}$$

Therefore, the mode is 34.61.