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In the following frequency distribution, the frequency of the class-interval (40-50) is missing. It is known that the mean of the distribution is 52. Find the missing frequency.

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answer is D.

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Detailed Solution

Given is a table,
Question Image

The expression for mean method is given as

x ¯ = ∑ f i x i ∑ f i

, where

f i x i

are the product of given numbers of data in table.
The mean of given data is 52.
Draw a table and obtain the class marks by using the formula

lowerlimit + upperlimit 2

So,

Here, the number of total observations is,

N = ∑ f i = 33 + f

Applying formula for mean method given as

x ¯ = ∑ f i x i ∑ f i

Then,

⇒ 52 = 1765 + 45 f 33 + f ⇒ 52 f − 45 f = 1765 − 1716 ⇒ f = 7

Thus, the value of f is 7.
Therefore, option (4) is correct.

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