Find the mode of the given data:

Class 20-29 30-39 40-49 50-59 60-69
Frequency 15 20 50 30 10

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Solution

Here the maximum class frequency is $50$ and the class corresponding to this frequency is $40 - 49$
So, the modal class is $40 - 49$
The lower limit of modal class $40 - 49$ is $l = 40$
Class size $c = 10$
Frequency of the modal class $f_{1} = 50$
Frequency of the class preceding the modal class $f_{0} = 20$
Frequency of the class succeeding the modal class $f_{2} = 30$

$\Rightarrow z = l + (\frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}}) \times c$
$= 40 + (\frac{50 - 20}{2 \times 50 - 20 - 30}) \times 10$
$= 40 + \frac{30}{50} \times 10$
$= 40 + 6$
$= 46$

$∴$ The mode for the given data is 46

Suggest Corrections

Marks	:	25-29	30-34	35-39	40-44	45-49	50-54	55-59
Frequency	:	4	5	23	31	10	8	5

Classes:	25−29	30−34	35−39	40−44	45−49	50−54	55−59
Frequency:	14	22	16	6	5	3	4

Age (in years)	0-9	10-19	20-29	30-39	40-49	50-59	60-69
No. of Persons:	5	15	20	23	17	11	9