For a data consisting of 15 observations x_i, | vedclass

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(B) Given,$\sum x = 170$ and $\sum x^2 = 2830$ for $n = 15$. Replacing the wrong observation $20$ with the correct observation $30$: Corrected $\sum x

Vedclass · Accepted Answer

$78$

Vedclass · Answer

(B) Given,$\sum x = 170$ and $\sum x^2 = 2830$ for $n = 15$. Replacing the wrong observation $20$ with the correct observation $30$: Corrected $\sum x = 170 - 20 + 30 = 180$. Corrected $\sum x^2 = 2830 - (20)^2 + (30)^2 = 2830 - 400 + 900 = 3330$. We know that,$	ext{Variance} = \frac{\sum x^2}{n} - \left(\frac{\sum x}{n}ight)^2$. Substituting the values: $	ext{Variance} = \frac{3330}{15} - \left(\frac{180}{15}ight)^2$. $	ext{Variance} = 222 - (12)^2$. $	ext{Variance} = 222 - 144 = 78$.

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