The mean of the following frequency distribution is `1.46.`

Find the missing frequencies.

Options

A. `76, 38`
B. `36, 75`
C. `39, 66`
D. `30, 79`

Answer

A

Explanation

Let the missing frequecines be p and q respectively . For calculating the mean, we prepare the table given below :

Here, ` sumf_(i) = 86 + p+q`
but , `sumf_(i) = 200` (given)
` 86 +p+q =200 Rightarrow p+q =114`
Also, mean ` (sum(f_(i) xx x_(i)))/(sumf_(i)) = (140 +p+2q)/(86 +p+q) = (140+114 +q)/(86 +114)`
` ( 254=q)/200`

But, mean = 1.46
`(254+q)/200 = 1.46 Rightarrow w254 +q = 292`
` Rightarrow q= 292 -254 =38`
putting q= 38 in (i), we get p=76
Hence, the missing frequencies are 76 and 38 respectively.