10 is the mean of a set of 7 observations and 5 is the mean of a set of 3 observations, the mean of the combined set is

Options

A. 15
B. 10
C. 8.5
D. 7.5

Answer

C

Explanation

Given mean of 7 observation is 10.
`therefore (x_(1)+x_(2)+……+x_(7))/(7)=10`
`rArr x_(1)+x_(2)+….+x_(7)=70" …(1)"`
Also, mean of 3 observations is 5.
`therefore(x_(8)+x_(9)+x_(10))/(3)=5`
`rArrx_(8)+x_(9)+x_(10)=15" ...(2)"`
So, from (1) and (2)
Required mean
`=(x_(1)+x_(2)+....+x_(7)+x_(8)+x_(9)+x_(10))/(10)`
`=(70+15)/(10)=(85)/(10)=8.5`