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Joined: Sep 2001
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Carpal Tunnel
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OP
Carpal Tunnel
Joined: Sep 2001
Posts: 6,296 |
On the chance that somebody here really does like math and understands mathematical terms well, I have a question about three of those terms.
In a nutshell, what is the difference between average, mean and median? Why would you use one over the other--in other words, why would you use an average over the mean?
If this is too complicated to discuss here, even though it's basic math, just ignore this thread altogether.
Also, I think I've got the three terms right, but, if I represented them not quite-on-target, just modify them. I just remember learning about average, mean, and median. It could have been average, mean and mode, but I don't think so...
Average, of course, was easy. Just a sum and then division. Good for making estimates for future predictions. Say, take a bunch of good recipes, compare ingredients, and devise a new recipe based on averages. That kind of thing. Or certainly grades in a grade book to find average grade.
But the other two--mean and median (if that's the term; could be mean and mode?)--I don't use them and suspect I probably should.
Anyway, please forgive if this is just to un-word-related.
Best regards,
WW
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Joined: Jul 2002
Posts: 7
stranger
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stranger
Joined: Jul 2002
Posts: 7 |
Here you go. Calling each number in the data-set a "term"
mode is the term that occurs most frequently.
median is the "middle" term. Arrange the terms in order in a line, and the median is the one in the middle of the line.
mean is the usual average. For the mean of n separate terms, add all the terms to get their sum, and then divide that sum by the number of terms (that is, divide by n). More exactly, that is the arithmetic mean.
For the geometric mean of n separate terms, multiply all the terms to get their product, and then take the nth root of that product.
All these will come to pretty much the same number if your data is distributed in the usual bell curve, but if it's not, the mean can paint a badly misleading picture of the data.
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old hand
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old hand
Joined: Nov 2000
Posts: 866 |
Good Q WW
I suffered my way through statistics and probability theory at uni but think there's still a bit of unscarred grey matter that can assist with the answers.
Average and mean are the same; derived from the sum of the elements (ie pieces of data) divided by the number of elements. I forget why mathematicians call it the mean (rather than the avaerage), maybe it was the alliterative qualities of the word - considering it is always used in conjunction with "mode" and "median". (BTW, "conjunction" is a mathematical term also!)
The median value of a data set is the middle value (once all the elements have been put in order). This is more useful to statisticians as far flung elements at either end of the data set tend to cancel each other out. Hence you get an "unskewed" value for the median - one that is unaffected by data which may be spurious or, if not spurious, irrelevant to the data set as a whole.
The "modal value" (or "mode") of a data set is the most common value - this is handy as it is not a function of the highest or lowest value in the data set.
I proffer this in the absence of Bean - she's the guru on this stuff - with a gift for presenting the answer so that we all can understand it!
stales
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Joined: Sep 2001
Posts: 6,296
Carpal Tunnel
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OP
Carpal Tunnel
Joined: Sep 2001
Posts: 6,296 |
Ah, I see now. Thanks very much for the definitions. I see that I was very wrong in that mean and average were one and the same. I think mode is the most interesting of the three--the ones that appears most frequently. I can't begin to imagine its practical application, but there must be many.
Thanks again to you both,
WW
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stranger
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stranger
Joined: Jul 2002
Posts: 6 |
They've answered your question about what does mean mean?
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Carpal Tunnel
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Carpal Tunnel
Joined: Dec 2000
Posts: 2,661 |
When teaching anger management (as I do so often) I ask participants to record the time of day and what it was that got them *upset. From this collected group information we determine our "mean mean meaning". 
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Joined: Sep 2001
Posts: 6,296
Carpal Tunnel
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OP
Carpal Tunnel
Joined: Sep 2001
Posts: 6,296 |
It seems in your time-of-day for anger data collecting, it would be interesting to note the most frequently occuring term, the mode, as I learned today. And wouldn't it be a mean surprise if that time of day was that falling in your anger management class! Ha!
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stranger
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stranger
Joined: Jul 2002
Posts: 7 |
>> From this collected group information we determine our "mean mean meaning".
You mean that by that means you determine our "mean mean meaning"?
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veteran
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veteran
Joined: Jan 2002
Posts: 1,526 |
I was on vacation and missed posting to this question. Everything Stales said is correct and I've nothing of substance to add - only a small thought.
We have a bunch of raw data - and the data is a pretty good reflection of itself. But looking at a big stack of numbers we often "miss the forest for the trees" and statistics is partly about trying to figure out some way of thinking about the data without thinking about all the components of the data - which we often aren't even capable of doing.
No single number like mean or mode or median is going to give us everything we need to know about the data. There are other things like standard deviation, skew, sample size - all important - but even these don't always cover it. In every case I know or can think of having a large sample size is good. Unfortunately, it's not always practical or possible - and this is where I get a little fuzzy with things and it starts looking like a black art.
k
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Pooh-Bah
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Pooh-Bah
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In reply to:
On the chance that somebody here really does like math and understands mathematical terms well...
Mathematics ... so unappreciated! There are so many wonderful mathematical terms for wordlovers to enjoy, either because the concepts that they express are so interesting, or else the words themselves are cool, such as "zeroth," the ordinal version of "zero." Not a bad word to have handy in a game of Scrabble, I imagine. Then there's "zepto," a prefix meaning 10 raised to the (-21st) power. (Perhaps not eligible in Scrabble as a mere prefix, but might merge well with "gram" or "meter.")
Then there's the lowly "e," perhaps the most common letter in English writing, and a mere 1 point in Scrabble, but in math it denotes the number equal to about 2.718281828, which is mostly notably the number for which the equation f(x)=a^x is equal to its own derivative. Granted, that sounds dry at first, but it means that functions expressed in those terms can go through derivations as easily as a ambassador with diplomatic priveliges can go through Customs. And how fascinating that e=(1/0!)+(1/1!)+(1/2!)+(1/3!)+(1/4!)+....
Of course that leads us to "!" which has nothing to do with surprise or alarm, but rather the factorial of a number, where 4!=1 x 2 x 3 x 4, and 5!=1 x 2 x 3 x 4 x 5 and so on. I admit that I can hardly see the term 6! without thinking "SIX!" before I remember, "oh, um..I mean, uh, six factorial."
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