Find the mode for the following frequency distribution.
Class $4 - 8$ $8 - 12$ $12 - 16$ $16 - 20$ $20 - 24$ $24 - 28$
Frequency $9$ $6$ $12$ $7$ $15$ $3$

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Solution

Here the maximum class frequency is $15$ and the class corresponding to this frequency is $20 - 24$ .
So, the modal class is $20 - 24$ .
The lower limit of modal class $20 - 24$ is $l = 20$ .
Class size c = 4; and frequency of the modal class $f_{1} = 15.$
Frequency of the class preceding the modal class $= f_{0} = 7$ .
Frequency of the class succeeding the modal class $f_{2} = 3$ .
$z = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times c$
$= 20 + (\frac{15 - 7}{2 \times 15 - 7 - 3}) \times 4$
$= 20 + \frac{8}{20} \times 4$
$= 21.6$
$∴$ The mode for the given data is $21.6$

Suggest Corrections

Class	0-4	4-8	8-12	12-16	16-20	20-24	24-28	28-32	32-36
Frequency	6	8	17	23	16	15	-	4	3

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	$4 - 8$	$8 - 12$	$12 - 16$	$16 - 20$	$20 - 24$	$24 - 28$
Frequency	$9$	$6$	$12$	$7$	$15$	$3$

Class-intervals	$0 - 4$	$4 - 8$	$8 - 12$	$12 - 16$	$16 - 20$	$20 - 24$
Frequency	$4$	$7$	$10$	$15$	$11$	$6$