In a set of consecutive ODD integers, the mean ALWAYS equals

Question

In a set of consecutive ODD integers, the mean ALWAYS equals the median.
In a set of consecutive EVEN integers, the mean ALWAYS equals the median.

True?

sidbidus · Answer

Yes, I think this is true.

Also
In a set of consecutive integers, the mean ALWAYS equals the median.

Mishari · Answer

FALSE 

 The Correct Statements: 
In a set of  an odd number of  consecutive ODD integers, the mean ALWAYS equals the median. 

In a set of  an odd number of  consecutive EVEN integers, the mean ALWAYS equals the median.

GMAT TIGER · Answer

true for all (even, odd or both) consecutive integers.

any example?

Pzazz · Answer

Both the stats

and

both stats hold good.....

EMPOWERgmatRichC · Answer

Hi All,

While this post originally goes back to 2007, and most (if not all) of the posters are probably gone, the questions posed are essentially Number Properties. They can ALL be proven by TESTing VALUES, although it does not appear that anyone went to the trouble of proving what they believed.

Here is the proof:

1) In a set of consecutive ODD integers, the mean ALWAYS equals the median.

Here are a series of examples to prove that this is TRUE.

{1, 3}
Mean = (1+3)/2 = 2
Median = (1+3)/2 = 2
Mean = Median

{1, 3, 5}
Mean = (1+3+5)/3 = 3
Median = 3
Mean = Median

{-3, -1, 1, 3}
Mean = (-3-1+1+3)/4 = 0
Median = (-1+1)/2 = 0
Mean = Median

{-5, -3, -1, 1, 3}
Mean = (-5-3-1+1+3)/5 = -1
Median = -1
Mean = Median

Using similar methods, you can also prove that the following is true:

2) In a set of consecutive EVEN integers, the mean ALWAYS equals the median.

GMAT assassins aren't born, they're made,
Rich

FGMATS · Answer

This is not correct. No matter the number of integers, the median and mean are the same in a set with consecutive integers. However, if the number of integers is odd, the mean=median=one of the numbers in the set, and if the number of integers is even, then mean=median but they don't equal one of the numbers in the set.

In a set of consecutive ODD integers, the mean ALWAYS equals

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In a set of consecutive ODD integers, the mean ALWAYS equals

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