Calculate the mode of the following frequency distribution:

Marks 0-10 10-20 20-30 30-40 40-50

Number of students 6 16 30 9 4

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Solution

As the class 20-30 has the maximum frequency, it is the modal class.

$∴ x_{k} = 20, h = 10, f_{k} = 30, f_{k - 1} = 16 and f_{k + 1} = 9 Mode, M_{0} = x_{k} + \{h \times \frac{(f_{k} - f_{k - 1})}{(2 f_{k} - f_{k - 1} - f_{k + 1})}\} = 20 + \{10 \times \frac{(30 - 16)}{(2 \times 30 - 16 - 9)}\} = 20 + \{10 \times \frac{14}{35}\} = (20 + 4) = 24$

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Similar questions

Calculate the mean for the following frequency distribution:

Marks	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80
Frequency	3	7	10	6	8	2	4

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	3	6	8	15	10	8

X

Marks	0−10	10−20	20−30	30−40	40−50	50−60
Frequency	12	18	27	?	17	6

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

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