If the mean of the following distribution is 26.2, then f is:

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answer is C.

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Detailed Solution

Given table is,
Question Image

We know,
The total sum of all the frequency is:

∑ f i = 10 + 12 + 5 + f + 15 ⇒ ∑ f i = 42 + f

Consider the table,
Question Image

The total sum of all the

x i f i

is :

∑ x i f i = 50 + 180 + 125 + 35 f + 675 ⇒ ∑ x i f = 1030 + 35 f

Now, using the formula

x ¯ = ∑ f i x i ∑ f i

x ¯ = ∑ f i x i ∑ f i ⇒ x ¯ = 1030 + 35 f 42 + f

According to the question,

26.2 = 1030 + 35 f 42 + f ⇒ 26.2 × (42 + f) = 1030 + 35 f ⇒ 1100.4 + 26.2 f = 1030 + 35 f ⇒ 35 f − 26.2 f = 1100.4 − 1030 ⇒ 8.8 f = 70.4 ⇒ f = 70.4 8.8 ⇒ f = 8

Therefore, the value of f is 8.
Hence, option 3 is correct.

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