Calculate the mode from the following data:

Marks 10−20 20−30 30−40 40−50 50−60 60−70

No. of Students 8 11 9 25 12 16

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Solution

Class Interval Frequency
(f)

10 − 20
20 − 30
30 − 40 8
11
9

f₀

40 − 50 25 f₁

50 − 60
60 − 70 12
16 f₂

By inspection, we can say that the modal class is (40 – 50) as it has the highest frequency of 25.
$Mode (Z) = l_{1} + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times i or, Z = 40 + \frac{25 - 9}{2 (25) - 9 - 12} \times 10 or, Z = 40 + \frac{16}{50 - 21} \times 10 or, Z = 40 + 5.517 = 45.52 Hence, mode (Z) is 45.52 .$

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Marks	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90
No of students	0	2	3	7	13	11	9	2	1

Marks	10−20	20−30	30−40	40−50	50−60	60−70
No. of Students	8	11	9	25	12	16

Marks	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Number of Students	2	18	30	45	35	20	6	3

Valuable	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	7	12	18	25	16	14	8