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

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CEO
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In a set of consecutive ODD integers, the mean ALWAYS equals [#permalink] New post 05 Nov 2007, 06:16
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?
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 [#permalink] New post 05 Nov 2007, 06:22
Yes, I think this is true.

Also
In a set of consecutive integers, the mean ALWAYS equals the median.
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 [#permalink] New post 05 Nov 2007, 13:17
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.
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Re: Concept: Consecutive Integers [#permalink] New post 05 Nov 2007, 21:01
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bmwhype2 wrote:
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?



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




Mishari wrote:
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.


any example?
Manager
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 [#permalink] New post 05 Nov 2007, 22:59
Both the stats

Quote:
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.


and

Quote:
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.


both stats hold good.....
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Re: In a set of consecutive ODD integers, the mean ALWAYS equals [#permalink] New post 01 Apr 2015, 13:36
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Re: In a set of consecutive ODD integers, the mean ALWAYS equals [#permalink] New post 01 Apr 2015, 19:21
Expert's post
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.

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Re: In a set of consecutive ODD integers, the mean ALWAYS equals   [#permalink] 01 Apr 2015, 19:21
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