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

Question

Dr. Abubacker · Accepted Answer

(a)
Given, n=15, $\Sigma x^{2} = 2830,\Sigma x = 170$
Since, one observation 20 was replaced by 30, then
$\Sigma x^{2} = 2830 - 400 + 900 = 3330$
And $\Sigma x^{\ } = 170 - 20 + 30 = 180$
Variance, $\sigma^{2} = \frac{\Sigma x^{2}}{n} - \left( \frac{\Sigma x}{n} ight)^{2}$=$\frac{3330}{15} - \left( \frac{180}{15} ight)^{2}$
$= \frac{3330 - 12 	imes 180}{15} = \frac{1170}{15} = 78.0$

Q. 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

Explanation

Reviewed by Dr. Abubacker

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