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

Question

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 (A) 44.00 (B) 44.46 (C) 45.00 (D) 45.54

Tardigrade Admin · Accepted Answer

Sum of 100 items =45 × 100=4500 Sum of items added =19+31=50 Sum of items replaced =91+13=104 New sum =4500-104+50=4446 ∴ New mean =(4446/100)=44.46

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

44.00

44.46

45.00

45.54

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

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