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  4. Mean of 100 observations is 45. It was later found that two observations 19 and 31 were in correctly recorded as 91 and 13. The correct mean is

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Q. Mean of $100$ observations is $45$. It was later found that two observations $19$ and $31$ were in correctly recorded as $91$ and $13$. The correct mean is

UPSEEUPSEE 2012

Solution:

Sum of $100$ items $=45 \times 100=4500$
Sum of items added $=19+31=50$
Sum of items replaced $=91+13=104$
New sum $=4500-104+50=4446 $
$ \therefore $ New mean $=\frac{4446}{100}=44.46 $