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Find the mode of the following data

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16.5

17.5

18

18.5

answer is B.

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Detailed Solution

Given data,
Question Image

8

is the highest frequency, modal class is

10 - 20

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

is lower limit of the modal class = 10

f_{1}

is frequency of the modal class = 8

f_{0}

is frequency of the class preceding the modal class = 5

f_{2}

is frequency of the class succeeding the modal class =7

h

is size of the modal class = 10
So,
Mode

= 10 + \frac{8 - 5}{2 (8) - 5 - 7} \times 10

\Rightarrow Mode = 10 + \frac{3}{16 - 12} \times 10

\Rightarrow Mode = 10 + \frac{3}{4} \times 10

\Rightarrow Mode = 10 + \frac{3}{2} \times 5

\Rightarrow Mode = 10 + 7.5

\Rightarrow Mode = 17.5

Thus, the mode is 17.5.
Hence, the correct option is 2.

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