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When is the mean = median?

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When is the mean = median? [#permalink] New post 24 May 2012, 12:04
From my understanding, mean = median if,
1. the set consists of evenly spaced numbers
2. if all the members of the set are equal
3. set has just one number

Is there any thing else? In DS type of "is mean = median" questions, what do you have to know to be sure that mean = median?
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Re: When is the mean = median? [#permalink] New post 24 May 2012, 19:17
Not true, here's an example where mean = median and none of your criteria listed are met.

{0,50,50,50,100}

For any evenly spaced set, the mean of the set is always equal to the median. But not vice versa!

Last edited by Cares on 24 May 2012, 20:13, edited 1 time in total.
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Re: When is the mean = median? [#permalink] New post 24 May 2012, 19:54
bellcurve wrote:
From my understanding, mean = median if,
1. the set consists of evenly spaced numbers
2. if all the members of the set are equal
3. set has just one number

Is there any thing else? In DS type of "is mean = median" questions, what do you have to know to be sure that mean = median?

Hi,

If a series is an arithmetic progression then mean value will always be equal to median, but vice versa is not true.

Thus, any series can be formed other than the ones you have mentioned where mean = median.
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Re: When is the mean = median? [#permalink] New post 25 May 2012, 05:44
Thanks guys!

I did not say that the list that I provided is the exhaustive list. I just wanted add more to it. So if the Q is "is mean=median" What constitute sufficiency other than arithmetic progression and/or evenly spaced sets? Anything about the relationship that can be expressed in terms of range, relationship between the smallest or largest number, or the relationship between median and other numbers etc.?
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Re: When is the mean = median? [#permalink] New post 31 May 2012, 11:03
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Perhaps the easiest way to understand when mean = median is this one reqiurement:

1) When the distribution above the mean is symmetrical to the distribution below the mean.

So think of the middle point. Whatever pattern of data you have above the middle point is mirrored on the other side (below) the middle point.

When this happens, the mean will effectively be the same as the median (the middle number by rank).

This is satisfied when data is evenly spaced out. It's also true in other mirror-like cases.

Sure the distribution does not necessarily have to be exactly mirrored on both sides. But as long as they roughly cancel each other out, then you'll have a situation where the mean = median.
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Re: When is the mean = median? [#permalink] New post 05 Jun 2012, 04:42
Median=Mean when:
1) Numbers are in a sequence i.e. evenly spaced (and that includes consecutive numbers)
2) Only one item in the set
3) All members of the set are equal

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Re: When is the mean = median? [#permalink] New post 05 Jun 2012, 22:23
I've always thought of it like this, if you take the average of a group of evenly spaced numbers and that result is the middle number, then voila, mean = median.

For instance,

10, 20, 30, 50, 70, 80, 90

Mean = 50
Median = 50

Last edited by vandygrad11 on 27 Mar 2013, 11:45, edited 1 time in total.
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Re: When is the mean = median? [#permalink] New post 08 Jun 2012, 09:48
When there's no skew in the distribution.....

It's nice if you check out intro statistics (say, AP)
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Re: When is the mean = median? [#permalink] New post 08 Jun 2012, 09:56
Simple explination,

Mean = median
When adding the diffence of every number from the mean in a set together = 0
example
(1,2,4,6,7)
Mean = 20/5 = 4

4-1=3
4-2=2
4-4=0
4-6=-2
4-7=-3

3+2+0-2-3=0
Re: When is the mean = median?   [#permalink] 08 Jun 2012, 09:56
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