variance uniqueness

Question

I got a list of N integers (without repetition) below 50, which always sum the same (so the mean is also the same) as the following:

[1,2,3, 10,20] , mean = 7.2

I can swap two numbers, and the mean will be 7.2 again:

[1,2,3, 11,19] , mean = 7.2

There is a way to find two list of this N integers with the same variance, or is it unique for all the possible combinations of N integers below 50?

As you are imposing just two constraints on $N$ numbers, this should be possible for all $N\ge2$. — , Jun 17 '16 at 10:00

score 0 · Accepted Answer · answered Jun 17 '16 at 14:01

0

$\{4,6,10,13,17\}$ and $\{3,7,10,14,16\}$ clearly have the same mean and variance and there will be other examples which are not so symmetric

$\{8,9,10,11,12\}$ is the only set of five distinct integers with its particular mean and variance

answered Jun 17 '16 at 14:01

Henry

Thanks, i appreciate the explanation with examples. – Ragnagard Jun 18 '16 at 18:16

1 Answers1