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If an experiment with 15 observations on $x$ the following results were available: $\Sigma x^2=2830 \: \Sigma x = 170$. One observation that was 20 was found to be wrong and was replaced by the correct value 30. The corrected variance is

$\begin {array} {1 1} (A)\;8.33 & \quad (B)\;78.00 \\ (C)\;188.66 & \quad (D)\;177.33 \end {array}$

 

1 Answer

Toolbox:
  • $ \large\frac{1}{n}$$ \Sigma x^{2} - \bigg( \large\frac{1}{n}$$ \Sigma x \bigg)^2$
Given: $ \Sigma x = 170 \: \Sigma x^2 = 2830$ and increase in $ \Sigma x=10$
$\Rightarrow\: \Sigma x' = 170+10=180$
Increase in $ \Sigma x^2=900-400=500$
$\Rightarrow\: \Sigma x'^2=2830+500=3330$
Correct Variance = $ \large\frac{1}{n}$$ \Sigma x^{'2} - \bigg( \large\frac{1}{n}$$ \Sigma x' \bigg)^2$
$ = \large\frac{1}{15}$$ \times 3330 - \bigg( \large\frac{1}{15} $ $\times 180 \bigg)^2$
$ = 222-144$
$ = 78$
Ans : (B)
answered Feb 1, 2014 by thanvigandhi_1
edited Mar 26, 2014 by rvidyagovindarajan_1
y u did 170 +10 = 180 and 900-400= 500
 

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