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

`78.00`

`188.66`

`177.33`

`8.33`

Text Solution

Verified by Experts

The correct Answer is:

`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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`(250)/(9)`

`(240)/(9)`

In an experiment with 10 observations on x the following results are available Sigmax^(2)=354 and Sigma x=58 . If one observation 8 that was found to be wrong and was replaced by the corrected value 10, then the corrected variance is

The mean of 20 observation is 12. On checking, it was found that two observation were wrongly copied as 3 and 6. If wrong observation are replaced by correct values 8 and 4, then the correct mean is

15.15

15.35