Question

In an experiment with 15 observations of x the following results were available `sum x^2=2830 sum x=170` one observation that was 20 was found to be wrong and it was replaced by its correct value of 30 Then the corrected variance is (1) `8.33` (2) `78` (3) `188.66` (4) `177.33`
A. `78.0`
B. `188.66`
C. `177.33`
D. `8.33`

Answer 1

Correct Answer - 1
Given n=15 ,`sumx^(2)=2830,sum x=170`
Since one observation 20 was replaced by 30, then
`sumx^(2)=2830-400+900=3330`
`sum x=170-20+30=180`
Var. `sigma^(2)=(sum x^(2))/(n)-((sum x)/(n))^(2)=(3330)/(15)-((180)/(15))^(2)=78`