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Calculate mode of the following data:

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answer is D.

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Detailed Solution

Given is a table,
Question Image

The formula to calculate the mode is,

Mode = I + f 1 − f 0 2 f 1 − f 0 − f 2 × h

, where I is the lower limit of the modal class,

f 1

is the frequency of the modal class,

f 0

is the frequency of the class preceding the modal class and

f 2

is the frequency of the class succeeding the modal class and h is the modal size.
It is observed that the maximum frequency is 12.
The modal class is, 40-60.
Here,

I = 40, f 1 = 12, f 0 = 10, f 2 = 6,

and

h = 20

.
So, the mode of the given data is,

⇒ Mode = 40 + 12 − 10 2 (12) − 10 − 6 × 20 ⇒ Mode = 40 + 28 × 20 ⇒ Mode = 45

Thus, the mode of the given data is 45.
Therefore, option (4) is correct.

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