Let me take a stab at providing a simple explanation. The terms average or mean are used interchangeably here.

Consider a set "A" with 3 numbers { 4, 4, 4}. The mean (or average) of this set is obviously 4.

Now lets extra extrapolate this a little bit.

Lets assume that we have 3 sets B, C, D.

Set B = 1, 3, 8 ==> Average = 4

Set C = 4, 4, 4 ==> Average = 4

Set D = 2, 6, 4 ==> Average = 4

When we "mix" sets with the same average (or mean), the average of the resultant set doesn't change. Lets "mix" sets B, C. The average of the resultant set is { 1, 3, 8, 4,4,4} is still 4

Lets "mix" sets C, D. The average of the resultant set { 4,4,4, 2, 6, 4, } is still 4.

Let's get back to {A} and assume that instead of containing 3 numbers, now A contained 3 subsets, with each subset having its own numbers.

So putting all of this together, if A comprised of 3 sets { {B}, {C}, {D} } and each of the sets {B}, {C}, {D} have the

same average, then the average of {A} will continue to remain the same. .

vinnativ wrote:

can someone provide a detailed explanation.

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