WHAT IS AVERAGE? MEAN vs. MEDIAN vs. MODE
What is average anyway?
When you read about the “average” for some data, you usually conjure the friendly and familiar arithmetical mean. This is the sum of scores divided by the number of scores that we all know and love. For example, the average for 32 + 6 + 5 + 4 + 3 is simply 50 ÷ 5, which works out to a nice neat 10. So why instead report the median—or in some cases the mode?
The median score
Well, if you imagine that those numbers represent the most recent bonuses (in thousands) of 5 people who make up a department in some company, then you might say that the average payout in that department was $10K, except that it clearly wasn’t. One guy—perhaps the owner’s son—got $32K while the other 4 came nowhere close to the arithmetical mean of $10K.
In this case the arithmetical mean is clearly unrepresentative of the data and a better statistic is the median. This is simply the middle score of the distribution, which is the number 5 in the case of 32 + 6 + 5 + 4 + 3. Using the median, you would say that the most-representative bonus for the department was $5K, and that $32K was “an outlier” (at the risk of understatement.)
Two real-life examples where the median is better used than the mean is for “average home sales” and “average car sales.”
- If 100 homes are sold in a city over a month, many will be mansions but most will not. The mansions will “skew” the arithmetical mean spuriously upward so that reporting “the median price of a home” is better representative.
- And it’s the same for cars: many more Toyotas will be in the distribution than BMWs, making the median price more representative than the mean.
The modal score
The mode is the score that occurs most frequently. Imagine that you take 2 pills every day, which would be 730 pills. Last year you missed 24 days so that your mean was 706 ÷ 365, which works out to 1.93 pills per day. If someone were to ask you how many pills you take a day, the mode would be more representative. You would say “2-a-day.” You do not take “1.93 per day.”
It is written: Statistics don’t lie, but liars use statistics
Unscrupulous people will report a mean, median, or mode in isolation and tout it as the “average” if it suits their purposes. This is why you should probe when someone starts talking about the “average” this or that. It’s also why better reports will include means, medians, and modes. If all three are in reasonable alignment, then you can speak confidently about “average.” But if there are large differences among them, then the data are skewed and require closer analysis to purport any central tendency.
Stephen G. Barone is a marketing communications specialist and co-principal at barodine marketing communications & research, a general contractor of creative and analytical marketing talent to the science, technology, engineering, medical, professional, and general business communities.
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