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Question

In an experiment with $$15$$ observations on $$x$$, then 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:


A
78
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B
188.6666
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C
177.3333
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D
8.3333
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Solution

The correct option is A $$78$$
Given that $$\sum x^2=2830$$ , $$\sum x=170$$

Given that one observation $$20$$ was replaced by $$30$$ 

Therefore,  $$\sum x=170-20+30=180$$ and
$$\sum x^2=2830-(20)^2+(30)^2=3330$$
Given that, number of observations $$n=15$$

Variance is given by $$\dfrac{\sum x^2}{n}-(\dfrac{\sum x}{n})^2$$

$$=\dfrac{3330}{15}-(\dfrac{180}{15})^2=\dfrac{3330-15*144}{15}$$

$$=\dfrac{1170}{15}=78$$

Mathematics

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