In an experiment with 15 observations on x, the following results were available ∑x2=2830 ∑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

∑x=170, ∑x2=2830 ∑x1=170−20+30=180 ∑x2=900−400=500 ∴∑12=2830−400+900=3330 σ2=1n∑x12−(1n∑x1)2 =333015−(18015)2=78

In an experiment with 15 observations on x, the following results were available ∑x2=2830 ∑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

∑x=170, ∑x2=2830 ∑x1=170−20+30=180 ∑x2=900−400=500 ∴∑12=2830−400+900=3330 σ2=1n∑x12−(1n∑x1)2 =333015−(18015)2=78

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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

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Detailed Solution

$\sum x = 170, \sum x^{2} = 2830 \sum x_{1} = 170 - 20 + 30 = 180 \sum x^{2} = 900 - 400 = 500 ∴ \sum_{1}^{2} = 2830 - 400 + 900 = 3330 σ^{2} = \frac{1}{n} \sum {x_{1}}^{2} - {(\frac{1}{n} \sum x_{1})}^{2} = \frac{3330}{15} - {(\frac{180}{15})}^{2} = 78$