Question

# In an experiment with 15 observation on x, the following results were available$$\sum x^{2}= 2830,\sum x=170$$ , one observation was that + 20 was found to be wrong and was replaced by the correct value 30, then the corrected variance is

A
188.66
B
177.33
C
8.33
D
78

Solution

## The correct option is B 78Incorrect $$\displaystyle \sum x^{2}=2830, n=15,\sum x=170+(30-20)=180$$ Correct $$\displaystyle \sum x^{2}=2830+(30)^{2}-(20)^{2}=2830+500=3330$$ $$\displaystyle \therefore$$ Correct variance is $$\displaystyle \sigma^{2} =\frac{\mbox{Corrected} (\sum x^{2})}{n}-\left(\frac{\mbox{Corrected} \sum x^{2}}{n}\right)^{2}$$ $$\Rightarrow \displaystyle \sigma^{2}=\frac{3330}{15}-\left(\frac{180}{15}\right)^{2}=222-144=78$$Mathematics

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