The mode of the following distribution is
Class Interval: 1-5 6-10 11-15 16-20 21-25
Frequency: 4 7 10 8 6

14.5

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16.5

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10.5

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13.5

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Solution

The correct option is C $13.5$
Modal group = 11-15 , since it has the highest frequency i.e $10$ .
Estimated Mode $M = L + \frac{f_{m} - f_{m - 1}}{f_{m} - f_{m - 1} + f_{m} - f_{m + 1}} \times w$

Lower class boundary of modal group $L = 10.5$
Frequency of group before the modal group $f_{m - 1} = 7$
Frequency of Modal group $f_{m} = 10$
Frequency of group after the modal group $f_{m + 1} = 8$
Group width $w = 5$

$∴ M = 10.5 + \frac{10 - 7}{10 - 7 + 10 - 8} \times 5$
$= 10.5 + \frac{3}{5} \times 5$
$= 13.5$
hence, option $D$ is correct.

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Similar questions

Class	:	1-5	6-10	11-15	16-20	21-25	26-30
Frequency	:	2	8	15	35	20	10

Class	1- 10	11-20	21-30	31-40	41-50
$f_{i}$	5	7	8	6	4

Four alternative options are given for each of the following statements. Select the correct option.

In an inclusive class interval (10 - 14), the lower real limit is:

A. 9.5

B. 10.5

C. 13.5

D. 14.5

Marks	1-5	6-10	11-16	16-20	21-25
No. of Students	7	10	6	32	24

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