For the following grouped frequency distribution find the mode:
Class: $3 - 6$ $6 - 9$ $9 - 12$ $12 - 15$ $15 - 18$ $18 - 21$ $21 - 24$
Frequency: $2$ $5$ $10$ $23$ $21$ $12$ $3$

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Solution

We observe that the class $12 - 15$ has a maximum frequency. Therefore, this is the modal class.

We have,
$l = 12, h = 3, f_{1} = 23, f_{0} = 10$ and $f_{2} = 21$
$Mode = l + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times h$

$\Rightarrow Mode = 12 + \frac{23 - 10}{46 - 10 - 21} \times 3$

$\Rightarrow Mode = 12 + \frac{13}{15} \times 3$

$\Rightarrow Mode = 12 + \frac{13}{5}$

$\Rightarrow Mode = 14.6$

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Similar questions

Q. What is the cumulative frequency of the modal class of the following distribution?

Class	3−6	6−9	9−12	12−15	15−18	18−21	21−24
Frequency	7	13	10	23	4	21	16

Q. Find the mode of the following data.

Number	$0 - 3$	$3 - 6$	$6 - 9$	$9 - 12$	$12 -$	$15 - 18$	$18 - 19$	$21 -$
Frequency	$4$		$9$	$7$	$6$	$3$	$1$

Construct a frequency table for the following ages (in years) of 30 students using equal class intervals, one of them being 9-12, where 12 is not included.
18, 12, 7, 6, 11, 15, 21, 9, 8, 13, 15, 17, 22, 19, 14, 21, 23, 8, 12, 17,15, 6, 18, 23, 22, 16, 9, 21, 11, 16.

Q. The mean of the following distribution is

18

. Find the frequency f of the class

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Class	$11 - 13$	$13 - 15$	$15 - 17$	$17 - 19$	$19 - 21$	$21 - 23$	$23 - 25$
Frequency	$3$	$6$	$9$	$13$	$f$	$5$	$4$

Prepare a frequency distribution by inclusive method taking class interval of 7 from the following data:

28	17	15	22	29	21	23	27	18	12	7	2	9	4
1	8	3	10	5	20	16	12	8	4	33	27	21	15
3	36	27	18	9	2	4	6	32	31	29	18	14	13
15	11	9	7	1	5	37	32	28	26	24	20	19	25
19	20	6	9

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Class:	$3 - 6$	$6 - 9$	$9 - 12$	$12 - 15$	$15 - 18$	$18 - 21$	$21 - 24$
Frequency:	$2$	$5$	$10$	$23$	$21$	$12$	$3$

28	17	15	22	29	21	23	27	18	12	7	2	9	4
1	8	3	10	5	20	16	12	8	4	33	27	21	15
3	36	27	18	9	2	4	6	32	31	29	18	14	13
15	11	9	7	1	5	37	32	28	26	24	20	19	25
19	20	6	9

28	17	15	22	29	21	23	27	18	12	7	2	9	4
1	8	3	10	5	20	16	12	8	4	33	27	21	15
3	36	27	18	9	2	4	6	32	31	29	18	14	13
15	11	9	7	1	5	37	32	28	26	24	20	19	25
19	20	6	9

For the following grouped frequency distribution find the mode:Class:3−66−99−1212−1515−1818−2121−24Frequency:25102321123

We observe that the class 12−15 has a maximum frequency. Therefore, this is the modal class.We have,l=12,h=3,f1=23,f0=10 and f2=21Mode=l+f1−f02f1−f0−f2×h⇒Mode=12+23−1046−10−21×3⇒Mode=12+1315×3⇒Mode=12+135⇒Mode=14.6

For the following grouped frequency distribution find the mode:
Class: $3 - 6$ $6 - 9$ $9 - 12$ $12 - 15$ $15 - 18$ $18 - 21$ $21 - 24$
Frequency: $2$ $5$ $10$ $23$ $21$ $12$ $3$

28	17	15	22	29	21	23	27	18	12	7	2	9	4
1	8	3	10	5	20	16	12	8	4	33	27	21	15
3	36	27	18	9	2	4	6	32	31	29	18	14	13
15	11	9	7	1	5	37	32	28	26	24	20	19	25
19	20	6	9