This was brought up in one of my classes today. What is the significance for the names of “mean” “median” and “mode”?
I can understand median a bit, since it’s in the middle. But mode? It sounds like “most” but not really…and then mean I just haven’t the faintest.
Anyone wanna help and help me (maybe) get extra credit?
What about looking in a dictionary that includes word origins/etymologies?
Both median and mean originate from the Latin medianus, meaning in the middle, the former by way of the Anglo-French meiene.
Mode is from the Latin modus, meaning measure.
I found all of this out using an amazing invention called a “dictionary.” (Ask your teacher.)
Ooops, misread the OP. Sorry!
The ‘median’ average is the middle figure when they are lined up in ascending order, and can sometimes be a more useful figure than the ‘mean’, which is what everyone thinks of as the “average” but which can be skewed by a single very large (or small) figure in the sample. The ‘mode’ average is the most numerous figure in the sample. It’s not generally very useful.
And “mode”, meaning the value or values that occur most often in the sample, connotes the word’s ordinary-language meaning of “trend” or “fashion”.
If everybody’s doing it, it’s the mode. Very modish. A la mode. See what I mean?
When there’s more than one value that occurs the largest number of times, then the sample has more than one mode: “bimodal”, “multimodal”, etc.
“Mean” and “median”, as others have pointed out, both literally indicate an average that’s “in the middle” of the sample values.
The “median” is the value EXACTLY in the middle, i.e., half the sample values are less than the median and half are greater. A “mean” of sample values is “in the middle” of them in a more general sense: it’s closer to the intermediate value(s) than to extreme ones.
In fact, the “mean” that you see in your statistics class (where you add up all the sample values and divide by how many of them there are) is only one kind of mathematical mean, namely, the so-called “arithmetic mean”. There are other kinds, such as the “geometric mean” and the “harmonic mean”, which you can google if you’re feeling curious.
Long time since I had to think of the mode, don’t think I’ve ever used it since school mathematics class
Thanks for the answer…though you didn’t have to be a dick about it.
I don’t know. In all senses (certainly all your examples) except the statistical one, “mode” pretty much means way, and can be replaced by way without much distortion. I do not see how that works for the statistical sense, however. It does not make much sense, to me, to call the most common value “the way” (whereas the trend and the fashion are the way people are doing things, and a la mode is the way to have your pie). Maybe the etymology is different.
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You may well have used it without calling it “the mode,” since it just means what’s most common or most typical—as in “The average person has ten toes” or “The average house on this street is one-story.”
Seems exactly parallel to me: the modal value is the (typical) way the values are. E.g., if a sample consists of the values {1, 7, 3, 2, 3, 5, 8, 3}, then 3 is the (typical) way the data show up.
I don’t know the precise origins of the technical term “mode” in statistics, but it doesn’t seem to me incongruous with those ordinary-language senses of “mode”.
I don’t think that actually answers the OP. Especially considering that median and mean have the same root - if you told a student to just look up the etymology then they’d be even more confused about what mean and median meant. And saying that ‘mode’ means ‘measure’ would be useless.
Another possibility is that the OP was looking for why those terms are used. For most mathematical terms, it’s because someone pioneered its use it in a publication, possibly with or without justification. Sometimes there are competing terms, but for whatever reason one of them becomes most common.
A good web resource is This list of origins of terms. “Mode”, in particular, dates to Karl Pearson in 1895.
I learned the meaning of “average”, “median” and “mode” (and more importantly how they differ, and why someone would use one instead of another) from Martin Gardner’s Aha-Insight a cute little cartoon book. Poke around with this Google books result (dial 2 pages back for the cartoon) and see if you want the book to clear it up for you better.
In several romance languages, the words for mode and fashion are actually the same one. The word for “way (=mode)” can be different or again the same. In Spanish they’re different, and RAE gives the one for mode/fashion as coming from French, while the one for way comes straight from Latin with no intermediate stops (ultimately, they all come from Latin).
The equivalent Spanish words make perfect sense when you look at how they’re used in other environments. Moda: the most common thing, what’s normal, what’s to be expected. Mediana: what’s in the middle (middle siblings, for example). Media: average.
Some corrections here:
–There is no such thing as a ‘median’ average. Median and average (or mean) are different things.
–The mode can be important for shoe and clothing stores. They need to know the most popular size of things.
The mean (or average), median, and mode are all measures of central tendency, i.e. where is the middle of the distribution. There are slight differences, and each has its use (though I admit the mode is the least useful). Since they are all trying to measure the middle, it shouldn’t be surprising that some have a common origin.
In my dissertation defense, there was an argument among the committee about whether the mean and the average are the same thing. An older prof said that the mean is a measure of a population, whereas the average is a measure from a sample from the population. The younger profs tended to think that the mean and the average are the same, as do I.
Huh, I would argue that “mean,” “median,” and “mode” are all types of averages, but when people talk about “average” they’re usually talking about the arithmetic mean.
Right, pulykamell. The mean, median and mode are routinely described as three different kinds of averages in elementary statistics (Ask Dr. Math and purplemath, for example).
mcgato is right that “average” is commonly used as synonymous with “arithmetic mean”, but wrong to claim that the term “average” can’t be correctly applied to the median and mode as well.
Yes, having those two different and somewhat contradictory senses of “average” in use simultaneously makes the term somewhat ambiguous and potentially confusing, but that’s just the way the average cookie crumbles.