Compute the mode for the following frequency distribution:
Size of items: 0-4 4-8 8-12 12-16 16-20 20-24 24-28 28-32 32-36 36-40
Frequency: 5 7 9 17 12 10 6 3 1 0

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Solution

Here, the maximum frequency is 17 and the corresponding class is $12 - 16$ . So, $12 - 16$ is the modal class.
We have,

$l = 12, h = 4, f = 17, f_{1} = 9$ and $f_{2} = 12$

$∴ M o d e = l + \frac{f - f_{1}}{2 f - f_{1} - f_{2}} \times h$
$\Rightarrow M o d e = 12 + \frac{17 - 9}{34 - 9 - 12} \times 4$

$\Rightarrow M o d e = 12 + \frac{8}{13} \times 4 = 12 + \frac{32}{13} = 12 + 2.4 = 14.4$

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Class interval:	0-8	8-16	16-24	24-32	32-40
Frequency:	$5$	$6$	$4$	$3$	$2$

C.I	0-4	4-8	8-12	12-16	16-20	20-24
frequency	4	7	10	15	11	6

class interval	0-4	4-8	8-12	12-16
frequency	4	8	5	6

Class interval:	0−8	8−16	16−24	24−32	32−40
Frequency:	5	9	10	8	8

Ages	24-28	28-32	32-36	36-40	40-44	44-48
No of teachers	12	10	15	9	8	6

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Size of items:	0-4	4-8	8-12	12-16	16-20	20-24	24-28	28-32	32-36	36-40
Frequency:	5	7	9	17	12	10	6	3	1	0