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The Arithmetic Mean of the following frequency distribution is 53 , then the value of p is,

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answer is D.

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Detailed Solution

Given 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 = 12 + 15 + 32 + p + 13 ⇒ ∑ f i = 72 + p

The total sum of all the

x i f i

is :

∑ x i f i = 120 + 450 + 1600 + 70 p + 1170 ⇒ ∑ x i f = 3340 + 70 p

Therefore,

x ¯ = ∑ f i x i ∑ f i ⇒ x ¯ = 3340 + 70 p 72 + p

We already know that the mean is 53.
Therefore, putting the mean in the formula we will find the value of mean in the formula we have:

53 = 3340 + 70 p 72 + p ⇒ 53 × (72 + p) = 3340 + 70 p ⇒ 3816 + 53 p = 3340 + 70 p ⇒ 70 p − 53 p = 3816 − 3340 ⇒ 17 p = 476 ⇒ p = 47617 ⇒ p = 28

The value of p is 28.
Therefore, option 4 is correct.

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