Question

Find the mode of the following distribution.

(i)

Class-interval:	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency:	5	8	7	12	28	20	10	10

(ii)

Class-interval:	10−15	15−20	20−25	25−30	30−35	35−40
Frequency:	30	45	75	35	25	15

(iii)

Class-interval:	25−30	30−35	35−40	40−45	45−50	50−55
Frequency:	25	34	50	42	38	14

(iv)

Class:	0−10	10−20	20−30	30−40	40−50	50−60	60–70
Frequency:	8	10	10	16	12	6	7

Answer 1

(i) Here, maximum frequency is 28 so the modal class is 40−50.

Therefore,

(ii) Here, maximum frequency is 75 so the modal class is 20−25.

Therefore,

(iii) Here, maximum frequency is 50 so the modal class is 35−40.

Therefore,

(iv)
Here, maximum frequency is 16 so the modal class is 30−40.

Therefore,

Lower limit of the modal class, l = 30

Width of the modal class, h = 10

Frequency of the modal class, f = 16

Frequency of the class preceding the modal class, f₁ = 10

Frequency of the class following the modal class, f₂ = 12

∴ Mode of the distribution

$$\begin{gathered} =l+\left(\frac{f-f_1}{2f-f_1-f_2}\right)\times h \\ =30+\left(\frac{16-10}{2\times 16-10-12}\right)\times 10 \\ =30+\frac{6}{10}\times 10 \\ =36 \end{gathered}$$

Hence, the mode of the distribution is 36.