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Question 15
Let ¯x be the mean of x1,x2,xn, and ¯y be the mean of y1,y2,yn. If ¯z represents the mean of x1,x2,xn,y1,y2,yn, then ¯z is equal to:

A) ¯x+¯y
B) ¯x+¯y2
C) ¯x+¯yn
D) ¯x+¯y2n


Solution

The answer is B.
Given, ni=1xi=n¯x and ni=1=n¯y(i)      [¯x=ni=1xin]
Now, ¯z=(x1+x2+xn)+(y1+y2++yn)n+n
=ni=1xi+ni=1yi2n
=n¯x+n¯y2n=¯x+¯y2   [from (i)]

Mathematics

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