When will mean and median be equal ?

[vinodhiniranganathan14]

Hi

I understand that the mean and median will be the same for evenly spaced sets.
For evenly spaced sets we can compute the mean as
(first term+last term)/2
However,for a statement that says "Average of n numbers is equal to the average of the largest and smallest numbers
in the set" ,we cannot conclude that the set is evenly spaced.But can we conclude that the mean and median for this set is the same ?
I have tried to make an exception for the statement,but in vain.

E.g,

0,0,10,10 mean=median=5,not evenly spaced
5,5,5,5 mean =median=5,evenly spaced
2,4,5,6,8 mean=median=5,not evenly spaced

Can someone please clarify if my inference is right ?

Thanks
Vino

[jnelson0612]

However,for a statement that says "Average of n numbers is equal to the average of the largest and smallest numbers
in the set" ,we cannot conclude that the set is evenly spaced.But can we conclude that the mean and median for this set is the same ?

Not necessarily. For example, imagine that n=5; we have five numbers in the set.

If the set is 1, 2, 3, 4, 5, the average of 1 and 5 is 3, which also happens to be the average of all the numbers in the set. This set has the same mean and median and is evenly spaced.

Now imagine a set of 2, 3, 9, 9, 12. The average of 2 and 12 is 7, which also happens to be the average of this set (sum is 35, 5 numbers, average 7). Although the average of the set is 7, the median is 9. Thus, the mean and the median are not the same.

I hope this helps!

[vinodhiniranganathan14]

Not necessarily. For example, imagine that n=5; we have five numbers in the set.

If the set is 1, 2, 3, 4, 5, the average of 1 and 5 is 3, which also happens to be the average of all the numbers in the set. This set has the same mean and median and is evenly spaced.

Now imagine a set of 2, 3, 9, 9, 12. The average of 2 and 12 is 7, which also happens to be the average of this set (sum is 35, 5 numbers, average 7). Although the average of the set is 7, the median is 9. Thus, the mean and the median are not the same.

I hope this helps!

Thanks for the reply.. I should have tried a few more examples..

[tim]

:)