Calculate the mode from the following data:

Marks(below) 15 30 45 60 75 90

No. of Students 10 30 60 84 90 100

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Solution

Class Interval Number of students
(c.f) Frequency
(f)

0 − 15
15 − 30 10
30 10
30 − 10 = 20 (f₀)

30 − 45 60 60 − 30 = 30 (f₁)

45 − 60
60 − 75
75 − 90 84
90
100 84 − 60 = 24 (f₂)
90 − 84 = 6
100− 90 = 10

By inspection, we can say that the modal class is (30 – 45) as it has the highest frequency of 30.
$Mode (Z) = l_{1} + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times i or, Z = 30 + \frac{30 - 20}{2 (30) - 20 - 24} \times 15 or, Z = 30 + \frac{10}{60 - 44} \times 15 or, Z = 30 + 9.375 = 39.375 Hence, mode (Z) is 39.375 .$

Suggest Corrections

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

Marks	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
No. of Students	2	18	30	45	35	20	6	3

X	0−10	10−20	20−30	30−60	60−90
Frequency	5	9	20	12	4

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