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 .

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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 . The corrected variance is

TestHub · Accepted Answer

Σ x = 170 , Σ x 2 = 2830 increase in Σ x = 10 , then Σ x ′ = 170 + 10 = 180 Increase in Σ x 2 = 900 − 400 = 500 then Σ x ′2 = 2830 + 500 = 3330 Variance = n 1 ​ Σ x ′2 − ( n 1 ​ Σ x ′ ) 2 = 15 1 ​ × 3330 − ( 15 1 ​ × 180 ) 2 = 222 − 144 = 78

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