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The mode of the following series is 50. Find the missing frequency in it

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15

16

12

answer is A.

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Detailed Solution

Given that the mode is 50 of the data,
Question Image

We know that,
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 = 30

h

is size of the class interval = 10

f_{1}

is frequency of the modal class = 16

f_{0}

is frequency of the class preceding the modal class = f

f_{2}

is frequency of the class succeeding the modal class = 12
Since the class

30 - 40

has the highest frequency

16

, it is the modal class.
Now,
Mode

= 30 + \frac{16 - f}{32 - f - 12} \times 10 = 50

⟹ 30 + \frac{16 - f}{20 - f} \times 10 = 50

⟹ \frac{16 - f}{20 - f} \times 10 = 50 - 30

⟹ \frac{16 - f}{20 - f} \times 10 = 20

⟹ 160 - 10 f = 400 - 20 f

⟹ 20 f - 10 f = 400 - 160

⟹ 10 f = 240

⟹ f = 24

Thus, the value of the missing frequency is 24.
Hence, the correct option is 1.

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