Mean and variance of $$20$$ observations are $$10$$ and $$4$$ respectively. It was found that in place of $$11$$, $$9$$ was taken by mistake. The correct variance, is

Question

Mean and variance of $$20$$ observations are $$10$$ and $$4$$ respectively. It was found that in place of $$11$$, $$9$$ was taken by mistake. The correct variance, is

Infinity Learn · Accepted Answer

Let $$x1$$,$$x2$$,…,$$x20$$ be $$20$$ observations. Then,           uncorrected ∑$$xi=20$$×$$10=200$$ and $$120$$∑$$xi2$$−$$(10)2=4$$⇒ uncorrected ∑$$xi2=2080$$    Corrected ∑$$xi=200$$−$$9+11=202$$     Corrected ∑$$xi2=2080$$−$$92+112=2120$$ ∴ Correct variance $$=120$$ Corrected ∑xi− Corrected ∑$$xi202$$                                  $$=212020$$−$$202202=106$$−$$102.01=3.99$$

Mean and variance of $20$ observations are $10$ and $4$ respectively. It was found that in place of $11, 9$ was taken by mistake. The correct variance, is

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Mean and variance of 20 observations are 10 and 4 respectively. It was found that in place of 11, 9 was taken by mistake. The correct variance, is

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Mean and variance of $20$ observations are $10$ and $4$ respectively. It was found that in place of $11, 9$ was taken by mistake. The correct variance, is