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The mean of the following distribution is 132 and the sum of the frequencies is 50, then the missing frequencies $f 1$ and $f 2$ .

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f 1 =

10,

f 2 =

f 1 =

20,

f 2 =

f 1 =

10,

f 2 =

f 1 =

f 2 =

answer is A.

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Detailed Solution

Given table is,
Question Image

Consider the table,
Question Image

We will use the formula,

x ¯ = a + ∑ f t u i ∑ f i × h

to find the mean of the given data.
We have,

∑ f i = 50 ⇒ ∑ f i = f 1 + f 2 + 32 ⇒ 50 = f 1 + f 2 + 32

∑ f i u i = 2 f 2 + 24

a =100
mean = 132
h =40
Now, mean,
⇒132=100+

24 + 2 f 2 50 × 40

⇒ 132 = 500 + 8 f 2 + 96 5 ⇒ 132 × 5 = 8 f 2 + 596 ⇒ 660 = 8 f 2 + 596 ⇒ 8 f 2 = 64 ⇒ f 2 = 8 Putting this value in (i), we get: f 1 + 8 = 18 ⇒ f 1 = 10

Therefore, the required frequencies are

f 1 =

10,

f 2 =

8.
Therefore, option 1 is correct.

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