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Find 'p’ if the mean of the given data is 15.45.

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answer is D.

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Detailed Solution

Given that mean is 15.45.
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 a table.
Draw a table and obtain the class marks by using the formula

lowerlimit + upperlimit 2

So,

Here, the number of total observations is

N = 30 + p

.
Applying the formula for mean method given as

x ¯ = ∑ f i x i ∑ f i

Then,

15.45 = 458 + 15 p 30 + p ⇒ 15.45 30 + p = 458 + 15 p ⇒ 463.5 + 15.45 p = 458 + 15 p ⇒ 15.45 p − 15 p = 458 − 463.5 ⇒ 0.45 p = 4.5 ⇒ p = 10

Thus, the value of

p

is 10.
Therefore, option (4) is correct.

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