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In an experiment with 15 observations on x, the following results were available $Σ x^{2} = 2830, Σ x=170$ one observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is

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answer is 78.

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Detailed Solution

We have $Σ x = 170, Σ x^{2} = 2830$

Increase in $Σ x = 10 \Rightarrow Σ x^{1} = 170 + 10 = 180$

Increase in $Σ x^{2} = 900 - 400 = 500 \Rightarrow Σ x^{2} = 2830 + 500 = 3330$

$∴ σ^{2} = \frac{1}{15} (3330) - {(\frac{1}{15} \times 180)}^{2} = 222 - {(12)}^{2} = 78$

$(∴ σ^{2} = \frac{Σ x^{2}}{n} - {(\frac{Σ x}{n})}^{2})$

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