Question about Evenly spaced set

[s.ashwin.rao]

I saw these rules for Evenly spaced set in the MGMAT guide be it for even number of items or odd number of items
1) Mean and Median are the equal and is average of first and last term.
2) Sum of all elements is multiple of number of items.

These rules work perfectly well for this set { 4, 8, 12, 16, 20, 24} but does not apply to set such as this {1, 2, 3, 4, 5, 6 } ?
I thought even this is a evenly spaced set with even difference of 1.

Thanks

[jnelson0612]

I saw these rules for Evenly spaced set in the MGMAT guide be it for even number of items or odd number of items
1) Mean and Median are the equal and is average of first and last term.
2) Sum of all elements is multiple of number of items.

These rules work perfectly well for this set { 4, 8, 12, 16, 20, 24} but does not apply to set such as this {1, 2, 3, 4, 5, 6 } ?
I thought even this is a evenly spaced set with even difference of 1.

Thanks

Hi Ashwin,
I think the first rule does apply to your second set {1, 2, 3, 4, 5, 6}. Let's check it out.

1) Mean and Median are the equal and is the average of the first and last term.

When I add those numbers I get a total of 21. Total/Number = Average, so 21/6 = 3.5. Notice that I also get 3.5 if I average 1 and 6 (7/2). Also notice that the median in this set would be the average of the two middle numbers, 3 and 4, because I have an even number of terms in my set. This also gives us 3.5.

2) Sum of all elements is multiple of number of items.

This is the rule ONLY if I have an odd number of elements in my set. If I have an even number of elements in my set the sum is NEVER a multiple of the number of elements in the set.