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In an experiment with 15 observations of...

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

`78.00`

B

`188.66`

C

`177.33`

D

`8.33`

Text Solution

Verified by Experts

The correct Answer is:
A
`sum x=170, sum x^(2)=2830`
The increase in `sum x` is 10, then
`sum x'=170+10=180`
The increase in `sum x^(2) " is" 900-400=500, `then
`sum x^(2)=2830+500=3330`
Variance`=(1)/(n) sum x^(2)-((1)/(2)sum x')^(2)^(2)`
`=(1)/(15)xx3330-((1)/(15)xx180)^(2)`
=222-144=78
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