In an experiment with 15 observations on x , the following results were available: x^2 = 2830 , x = 170 . One observation that was 20 was found to be - Mathematics MCQ AIEEE-CBSE-ENG-03 2026 | ExamTest.live

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In an experiment with 15 observations on x, the following results were available: \sum x^{2} = 2830, \sum 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:

Solution & Step-by-step Explanation

Corrected \sum x = 170 - 20 + 30 = 180 . Corrected \sum x^{2} = 2830 - 2 0^{2} + 3 0^{2} = 2830 - 400 + 900 = 3330 . Number of observations n = 15 . Corrected Variance σ^{2} = \frac{\sum x ^{2}}{n} - (\frac{\sum x}{n})^{2} $ σ^{2} = \frac{3330}{15} - (\frac{180}{15})^{2} = 222 - (12)^{2} = 222 - 144 = 78 $

Try it yourself before checking the explanation above.

In an experiment with 15 observations on x, the following results were available: \sum x^{2} = 2830, \sum 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:

78.00

188.66

177.33

8.33

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