Find the mode of the following frequency distribution:

Class interval 0-4 4-8 8-12 12-16

Frequency 4 8 5 6

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Solution

As the class interval 4-8 has the maximum frequency, it is the modal class.

$∴ x_{k} = 4, h = 4, f_{k} = 8, f_{k - 1} = 4, f_{k + 1} = 5 Mode, M_{0} = x_{k} + \{h \times \frac{(f_{k} - f_{k - 1})}{(2 f_{k} - f_{k - 1} - f_{k + 1})}\} = 4 + \{4 \times \frac{(8 - 4)}{(2 \times 8 - 4 - 5)}\} = 4 + \{4 \times \frac{4}{7}\} = (4 + 2.29) = 6.29$

Suggest Corrections

Class interval:	0–4	4–8	8–12	12–16	16–20
Frequency	4	6	8	5	2

Class Interval	4−8	8−12	12−16	16−20	20−24	24−28	28−32	32−36	36−40
Frequency	10	12	16	14	10	8	17	5	4

Class-interval	0−4	4−8	8−12	12−16	16−20	20−24
Frequency	10	15	20	25	20	10

Variable (x_i)	4	6	8	10	12
Frequency (f_i)	4	8	14	11	3