Question

The mean of 40 observations was 160. It was detected on rechecking that the value of 165 was wrongly copied as 125 for computation of mean. Find the correct mean.

Answer 1

Here, n = 40, `bar"X" = 160`.
So, `bar"X" = (1)/"n"(sumx_i)`
⇒ 160 = `(1)/(40)(sumx_i)`
⇒ `sumx_i` = 160 x 40 = 6400
∴ Incorrect value of `sumx_i = 6400`.
Now, correct value of 
`sumx_i` = Incorrect value of `sumx_i` - Incorrect item + Correct item
= 6400 - 125 + 165
= 6440
∴  Correct mean
= `("Correct value of" sumx_i)/"n"`
= `(6440)/(40)`
= 161.