Question

the mean of 25 observations is 27. if one observation is included, the mean still remains 27. find the included observation

Answer 1

Hi there,

The answer is 27

mean = 27
sum of all observations = 27 *25
now when new observation is added then
mean = 27 (remains same is given)
sum of all observations = 27(25+1)

now sibtract both the sums to get the added observation value
27*26 - 27*25
= 27

Hope it helped you.
Let me know if any further doubt.
Cheers !!!

Answer 2

Mean=sum of observations/number of observations

27=sum of obs./25

27*25=sum of obs

Sum of all obs=675

Let the obs which us added be equal to x

So the mean remains the same(given)

27=(675+x)/26

27*26=675+x

702-675=x

27=x

The observation which when added to the data keeps the mean unchanged is 27

The new no. of observations will be 26 and the total of all observations will be 27