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Manager
Joined: 19 Nov 2010
Posts: 82
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When is the mean = median?
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 24 May 2012, 13:04
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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Manager
Joined: 21 May 2012
Posts: 88
Location: United States (CA)
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Re: When is the mean = median?
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Updated on: 24 May 2012, 21:13
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!
Originally posted by Cares on 24 May 2012, 20:17.
Last edited by Cares on 24 May 2012, 21:13, edited 1 time in total.
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Current Student
Joined: 29 Mar 2012
Posts: 302
Location: India
GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38
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Re: When is the mean = median?
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24 May 2012, 20:54
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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Manager
Joined: 19 Nov 2010
Posts: 82
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Re: When is the mean = median?
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25 May 2012, 06:44
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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SVP
Joined: 14 Apr 2009
Posts: 2283
Location: New York, NY
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Re: When is the mean = median?
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31 May 2012, 12:03
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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Manager
Joined: 15 Sep 2009
Posts: 195
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Re: When is the mean = median?
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05 Jun 2012, 05:42
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 Cheers.
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+1 Kudos me - I'm half Irish, half Prussian.
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Senior Manager
Joined: 13 Jan 2012
Posts: 280
Weight: 170lbs
GMAT 1: 740 Q48 V42 GMAT 2: 760 Q50 V42
WE: Analyst (Other)
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Re: When is the mean = median?
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Updated on: 27 Mar 2013, 12:45
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
Originally posted by geometric on 05 Jun 2012, 23:23.
Last edited by geometric on 27 Mar 2013, 12:45, edited 1 time in total.
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Manager
Joined: 01 May 2012
Posts: 56
Location: Canada
GPA: 1
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Re: When is the mean = median?
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08 Jun 2012, 10:48
When there's no skew in the distribution.....
It's nice if you check out intro statistics (say, AP)
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Director
Status: Can't wait for August!
Joined: 13 Sep 2011
Posts: 985
Location: United States (MA)
Concentration: Marketing, Strategy
GMAT 1: 660 Q44 V37 GMAT 2: 680 Q45 V38 GMAT 3: 710 Q45 V42
GPA: 3.32
WE: Information Technology (Retail)
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Re: When is the mean = median?
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08 Jun 2012, 10:56
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
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Intern
Joined: 24 Sep 2016
Posts: 34
Location: United States (CT)
Concentration: Finance, International Business
GPA: 3.81
WE: Analyst (Venture Capital)
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Re: When is the mean = median?
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22 Feb 2017, 22:41
There are specific rules which allow you to determine when the mean equals the medium but it's better to just mathematically out the set of numbers together. The median will always be the middle value regardless of the set. If it's even amount of numbers it will be the average of the two middle numbers. If you add up all the numbers determine the mean and if it is equal to the middle value. The mean = the median.
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Joined: 09 Sep 2013
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Re: When is the mean = median?
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17 Sep 2018, 12:45
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Re: When is the mean = median?
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17 Sep 2018, 12:45
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