Question

If x is the mean of x₁,x₂............xⁿ and y is the mean of y₁, y₂,…….yn and z is the mean of x₁,x₂............xn , y₁, y₂,……….yⁿ then z =? Write the correct alternative answer for the question.
(A)x +y/2
(B)x+y
(C)x+y/n
(D)x+y/2n

Answer 1

Given ,

x is the mean of x1 , x2 , ... , xn

Sum of n observations of x = xn ...(1)

y is the mean of y1 , y2 ,........., yn

Sum of n observations of y = yn .

Now ,Z is the mean of all observations of x ,y .

We know that ,

Mean = Sum of observations / Number of observations .

So ,

Z = nx + ny / ( n + n )

Z = n ( x + y ) / 2n

Z = x + y /2 .

Therefore ,The correct relation is Z = x + y /2 .

Ans : Option A

Answer 2

Option ( A ) is correct.

Explanation :

Given , mean of xn terms = x

Mean if y1,y2 , ...,yn = y

Therefore ,

z = ( x + y )/2

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