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The following table gives weekly wages in rupees of workers in a certain commercial organization. The frequency of class 49-52 is missing. It is known that the mean of the frequency distribution is 47.2, then the missing frequency is,

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answer is C.

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Detailed Solution

Given frequency table is,
Question Image

Consider the table,
Question Image

From the table, we will find the midpoint of the classes which will be

x i

and from then we will find

x i f i

from the table.
The total sum of all the frequency is:

∑ f i = 31 + 58 + 60 + p + 27 ⇒ ∑ f i = 176 + p

The total sum of all the

x i f i

is :

∑ x i f i = 1286.5 + 2581 + 2850 + 50.5 p + 1444.5 ⇒ ∑ x i f i = 8162 + 50.5 p

Therefore,

x ¯ = ∑ f i x i ∑ f i ⇒ x ¯ = 8162 + 50.5 p 176 + p

We already know that the mean is 47.2.
Therefore, putting the mean in the formula we will find the value of mean in the formula we have:

47.2 = 8162 + 50.5 p 176 + p ⇒ 47.2 × (176 + p) = 8162 + 50.5 p ⇒ 8307.2 + 47.2 p = 8162 + 50.5 p ⇒ 50.5 p − 47.2 p = 8307.2 − 8162 ⇒ 3.3 p = 145.2 ⇒ p = 145.2 3.3 ⇒ p = 44

The value of the missing frequency is 44.
Therefore, option 3 is correct.

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