Find the mode of the marks obtained by 80 students in a class test in English as given below:

Marks 0-10 10-20 20-3 30-40 40-50 50-60 60-70 70-80

Number of
students 3 5 16 12 13 20 6 5

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Solution

As the class $50 - 60$ has the maximum frequency, it is the modal class.
Now, $x_{k} = 50, h = 10, f_{k} = 20, f_{k} - 1 = 13, f_{k} + 1 = 6$
Now,
Mode $= x_{k} + [(f_{k} - f_{0}) / (2 f_{1} - f_{0} - f_{2})] \times h$
$= 50 + [(20 - 13) / (2 \times 20 - 13 - 5)] \times 10 = 50 + [(7) (5 / 40 - 18) \times 10] = 50 + [(7 \times 10) / 22]$
$= 50 + 3.18$
$= 53.18$

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Marks	10−20	20−30	30−40	40−50	50−60	60−70	70−80	80−90	90−100
Number of Students	4	10	16	22	20	18	8	2	5

Marks	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Number of Students	5	7	15	25	20	15	8	5

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 Obtained	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Number of Students	10	16	20	20	22	15	8	5

Marks	0-10	10-20	20-3	30-40	40-50	50-60	60-70	70-80
Number of students	3	5	16	12	13	20	6	5

Marks	10-20	20-30	30-40	40-50	50-60	60-70	70-80
Number of students	6	8	13	7	3	2	1