Question

The mean of 25 observations is 27...If one more observation is added or included, the mean still remains 27..Find the included observation and the total of all the frequencies (observations)...

Answer 1

Heya

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 702

Answer 2

x/25=27
x=25*27. (1)
(x+y)/26=27
(x+y)/26=x/25
y/26=x(26-25)/650
y/26=x/650
y=x/25
y=(25*27)/25. from (1)
y=27