Find out mode from the following data:

Size 0−4 4−6 6−10 10−15 15−20 20−30 30−35 35−40

Frequency 2 4 3 5 2 20 6 8

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Solution

In the given question, class intervals are not equal. For the calculation of mode, first the class intervals are made equal and frequencies are adjusted assuming that frequencies are equally distributed. In this manner, we get the following distribution.

Class Interval Frequency
(f)

0 − 10
10 − 20
20 − 30
30 − 40 9
7 (f₀)
20 (f₁)
14 (f₂)

By inspection, we can say that the modal class is (20 – 30) as it has the highest frequency of 20.
$Mode (Z) = l_{1} + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times i or, Z = 20 + \frac{20 - 7}{2 (20) - 7 - 14} \times 10 or, Z = 20 + \frac{13}{40 - 21} \times 10 or, Z = 20 + \frac{130}{19} or, Z = 20 + 6.84 = 26.84 Hence, mode is 26.84 .$

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Class-Interval	0−5	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Frequency	5	7	15	18	16	9	6	3

Class	5-10	10-15	15-20	20-25	20-30	30-35	35-40	40-45
Frequency	5	6	15	10	5	4	2	2

Class interval	1-5	6-10	11-15	16-20	21-25	26-30	31-35	36-40	41-45	46-50
Frequency	3	8	13	18	28	20	13	8	6	4

Size	0−4	4−6	6−10	10−15	15−20	20−30	30−35	35−40
Frequency	2	4	3	5	2	20	6	8

Class Interval	Frequency (f)
0 − 10 10 − 20 20 − 30 30 − 40	9 7 (f₀) 20 (f₁) 14 (f₂)

Class Interval	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Number of Children	4	5	3	2	6	7	3