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I have a bunch of statistical data and I want to present a short summary to the user (non-technical consumer). Now I want to show an average and need to decide between arithmetic mean and median. From a mathematical point of view, the median would be better due to the possibility of outliers skewing the average.

But I'm unsure if users understand the word and concept median. I suspect, many users don't know the difference between the two and think of the mean when they hear average.

So, should I use the mean (possibly more easy to understand) or the median (possibly better for interpretation)? Or maybe I could use the median but call it average? But that might confuse or deceive people, or not?

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Mean / median was what, the 2nd or 3rd grade? Why would your readers have issue with this even not being technical? –  Austin French Jun 6 '13 at 16:53
    
Don't use median and call it the average - they have different definitions and you would confuse people who do know the difference. If you want to exclude outliers in a dashboard, just put a tiny subtle note somewhere on the page to indicate that. –  Karen Jun 6 '13 at 17:14
    
Do you think the general public understand the word "mean"? I see no problem with calling the median "average" (it is an average, after all). –  Brendon Jun 6 '13 at 18:46
    
How about "expected value"? –  CJ Franken Jun 6 '13 at 19:48
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Does the median user understand the average? –  Neil McGuigan Jun 11 '13 at 18:00
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10 Answers 10

You can use the term "mean" which is fairly easy to understand. The term median is not that much easy. If it is used then it should be accompanied with the description, which may or may not be understood by the simple/novice/non-mathematical user.

Instead of deceiving people(as you are thinking) it will be great if the simpler terms are used than the more technical. User will be obviously interested in using the system which is more user friendly and simple to understand.

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I would use the math that displays the necessary data, and use the proper term as well as perhaps explain or use the long name.

An Average is, to me an arithmetic mean. I believe this is regional, so if you use Average ( a + b + c / 3) or mean adjust it per your region or use the long-name arithmetic mean.

If you use Median, and are worried about your users then call it something else that seems more explanatory. Median has always been an easy concept to me because we also have medians in the middle of the street, thus median is middle.

Other terms that could be used for Median

  • Midpoint
  • Middle Number
  • Center

The only problem I have, as someone who does understand median is that with an even number of numbers you must calculate the median:

1, 5, 9 and the median is 5. With :

1 5 9 15 then the median is (5 + 9) / 2 or 7. In the grand schemes, it is a tiny difference, but if it were called a midpoint and I noticed there was no 7 in your data series it would be worrisome.

A non-technical person would probably skim over these details entirely though, which leads me to think that if a majority would understand something like middle number better than median then use median, but mark it up in a way so that it can be easily understood (Perhaps with asterisks and a note) that * denotes an approximate number, or a calculated median.

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Actually, there are 3 different ways to calculate the median of an even number of numbers: the lower median, the upper median and the average of these two. The latter is used most often, but sometimes you need to guarantee that the median is an element of the numbers. –  Sebastian Negraszus Jun 13 '13 at 8:36
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I would use the term "Average (median)" if there was enough real estate for it, but if it is easy to ask the users, then do that first.

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Average and median are completely different calculations. If you cannot explain the difference to the user, you should atleast not try to teach them a wrong thing. –  rk. Jun 12 '13 at 18:11
    
@rk. I think you're wrong there, Median is an average, just as the mean and mode are averages. They're not totally different calculations. –  JonW Jun 12 '13 at 18:23
    
@JonW Median will be the center of the range. Average is the sum of the range divided by the length of the range. Can be same in some cases, but, not the same thing. –  rk. Jun 12 '13 at 18:26
    
@rk An average is defined as any of mean, median or mode. –  Jool Jun 12 '13 at 18:33
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@Jool Nvm, I was stuck with the first definition, but, seems it is loosely defined in general usage. en.wikipedia.org/wiki/Average For me, average = arithmetic mean. –  rk. Jun 12 '13 at 18:38
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I think your instinct to provide a median is likely the correct one, as it generally matches the way people think about skewed data sets (in 2004, for example, the mean US income was nearly 40% higher than median).

Are you in a position to educate your users? If so, use "median" because it is the most accurate, and provide a sidebar, tooltips, or linked information defining the word in simple terms.

Otherwise, you might consider another term, depending on the sort of data with which you're dealing. I like "midpoint" as a label used in a graphic. It can be clear, especially in context. You might also just label something as the "middle score" (or similar).

If you are speaking to your user in complete sentences, then you can use the even more well-understood concept of 50%. That is, "50% of the US population earns an annual income of $49,777 or less."

If this is a much more casual sort of statistic, consider using the phrase, "in general" or "generally." That is, you might say, "In general, users take around 48 seconds to complete our survey."

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Can you include a simple description when the user selects? Something like this:

  • Show the mean average: the total of all the responses, divided by the number of responses
  • Show the median average: the middle value when all responses are put in order

Think this needs to be tested with your users!

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  1. Technically, the word "average" means "damage to a ship". †

  2. Mean has a variety of problems, such as outliers, and Median is much more robust.

  3. I would say most people would think mean when you say average, and not median

  4. Consider another term, such as Centrality or Middle of the distribution.

  5. Someone with some statistical knowledge might want to see both, as when mean and median diverge, you know the distribution is skewed.

† Lloyd's of London started in a coffee shop in London where people would bet on ships sinking, then started pooling their bets (sharing the average), creating insurance.

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Ask the users! :)

Ask some "non-technical consumers" whether they understand the term "median" to get an idea of how many people will / won't get it.

If, in your eyes there are enough people who don't understand, include a brief explanation the first time you use the term.

I disagree with PeterL's advice. Do not assume that you know what the reader is looking for based on their understanding of the term.

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Don't use technical terms (jargon) for a general audience. Use average as your primary label, and if you want more information to be available on the type of average you are using, common solutions are parentheses, or an asterisk and a footnote:

e.g. Average (median).

e.g. Average*

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If the better thing to show is the median, show the median and call it the median.

If they don't know what it is, they probably won't appreciate the difference anyway. If they do know what it is, they'll appreciate you clarifying you mean median and not mean.

If they don't know that a median is a type of average, they probably aren't mathy enough to really do much with the numbers anyway, they're just looking for general trends at best. If you are worried that your users might both

  • Really want to see an "average", and
  • Not know that a median is a type of average,

then make the first occurrence of the term "median" a link with a tooltip/popup that defines it for them, making sure to start with "A median is an average of numbers..." or something similar.

I think the big thing is you don't want to call it an average and provide a median -- while this is correct, you can see even just in the comments on your question that the term "average" for some people means "arithmetic mean". While a median is an average, most people are so used to it meaning "mean" that they may make incorrect assumptions.

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Who is your audience? That's going to be depend on whether it's for the general public or, say, academics.

Why can't you show the average and have it actually be the average?

I'd guess that most people are not going to know the mean or the median. If you must show either one I think you're going to need a tool tip or some kind of explanation of what the term means. But again, that depends on your audience.

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I think this would be a better comment, as it really answer little. –  Austin French Jun 6 '13 at 16:54
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