Find the mode of the following distribution:

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38.33

98.33

78.7

74.69

answer is A.

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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.
As 35-40 class interval has highest frequency, it is the modal class.
Therefore, the modal class is 35-40.

Mode = 1 + f 1 − f 0 2 f 1 − f 0 − f 2 × h ⇒ Mode = 35 + 50 − 34 2 × 50 − 34 − 42 × 5 ⇒ Mode = 35 + 16 100 − 34 − 42 × 5 ⇒ Mode = 35 + 1624 × 5

Therefore,

⇒ Mode = 35 + 23 × 5 ⇒ Mode = 105 + 10 3 ⇒ Mode = 1153 ⇒ Mode ≈ 38.33

Thus, the mode of the given distribution is 38.33.
Therefore, option (1) is correct.

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