Question

Mean of 100 observations is 40. The 9th observation is 30. If this is replaced by 70 keeping all other observations same, find the new mean. Write the correct alternative answer for the question.
(A) 40.6
(B) 40.4
(C) 40.3
(D) 40.7

Answer 1

we know that

Mean = sum of terms/ no.of terms

Given Mean = 40

Given no.of terms = 100

subsitute this information in mean formula

we get

40= sum of terms / 100

sum of terms = 100(40)
sum of terms= 4000

Given additional information in the question is that 9th observation is 30 and should be replaced with 70 keeping remaining observations unchanged

So now correct sum of terms will be
4000 - 30 + 70 = 4040

New mean
= sum of corrected observations/ no. of terms
=4040 / 100
=40.4 is the new mean...

So option 'B' is the correct answer....

Answer 2

Option ( B ) is correct.

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Before solving, lets see a Formula,


$mean \: = \frac{sum \: of \: observation}{total \: number \: of \: observations}$


According to the question :



$=> 40 = \frac{sum \: of \: 100 \: observations}{100}$

=> 4000 = sum of observations ----1equation




In 4000 observations, there was a observation 9th ( 30 ) which was replaced by 70



So, new sum of observations => 4000 + 70 - 30

=> New sum of observations => 4040




Hence,


New mean = 4040 ÷ 100

New mean = 40.4