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Class Interval
0-10
10-20
20-30
30-40
40-50
Frequency
6
9
10
4
2

Find the mode of the following data.

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16.5

21.43

18

18.5

answer is B.

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Detailed Solution

Given data,

Class Interval	0-10	10-20	20-30	30-40	40-50
Frequency	6	9	10	4	2

10

is the highest frequency, modal class is

20 - 30

and the mode lies in this class
Now, Mode

= l + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times h

Where,

l_{1}

lower limit of the modal class.

l

is lower limit of the modal class = 20

h

is size of the class interval = 10

f_{1}

is frequency of the modal class = 10

f_{0}

is frequency of the class preceding the modal class = 9

f_{2}

is frequency of the class succeeding the modal class = 4
So,
Mode

= 20 + \frac{10 - 9}{2 (10) - 9 - 4} \times 10

\Rightarrow Mode = 20 + \frac{1}{20 - 13} \times 10

\Rightarrow Mode = 20 + \frac{1}{7} \times 10

\Rightarrow Mode = 20 + 1.43

\Rightarrow Mode = 21.43

Thus, the mode of the given data is 21.43.
Hence, the correct option is 2.

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