From the following data of the ages of different persons, determine the modal age.

Age (in years) 10−20 20−30 30−40 40−50 50−60 60−70 70−80

No. of Persons 4 26 32 10 9 6 3

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Solution

Age(in years)
(X) Number of Persons
(f)

10 − 20
20 − 30
30 − 40
40 − 50
50 − 60
60 − 70
70 − 80 4
26 f₀
32 f₁
10 f₂
9
6
3

By inspection, we can say that the modal class is (30 – 40) as it has the highest frequency of 32.
$Mode (Z) = l_{1} + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times i or, Z = 30 + \frac{32 - 26}{2 (32) - 26 - 10} \times 10 or, Z = 30 + \frac{6}{64 - 36} \times 10 or, Z = 30 + 2.14 = 32.14 Hence, mode (Z) is 32.14 years .$

Suggest Corrections

Age	20−25	25−30	30−35	35−40	40−45	45−50	50−55	55−60
No. Persons	50	70	100	180	150	120	70	60

Age (in years)	10−20	20−30	30−40	40−50	50−60	60−70	70−80
No. of Persons	4	26	32	10	9	6	3

Age(in years) (X)	Number of Persons (f)
10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70 70 − 80	4 26 f₀ 32 f₁ 10 f₂ 9 6 3

Marks	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
No. of persons	5	10	20	40	30	20	10	4

Age in years (below)	10	20	30	40	50	60	70	80
No. of persons	15	30	53	75	100	110	115	125