Talk:Average

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Notice postied on EdPoor's page:


I noticed that you edited out my (correct) version of average, and replaced it with the previously (incorrect) one, labelling my version as obscure. This confirms for me what I have been thinking for some time, that the entire CP project is doomed, unless you and other Sysops get a bit more open-minded, and read the entries that others have written and are prepared to learn, rather than be dogmatic. I defined Average, exactly as I would define it to my students; the point is, that in common parlance, people use average as the middle or most likely of set of data, without actually understanding that the idea is problematic. As it turns out, the most sensible 'middle' is actually the median, and the most common is the mode; however, neither of these are what people normally refer to as "the average"; notmally they calculate it using the arithmetic mean. However that is neither the most common, nor the middle. Can you provide an explanation what the arithmetic mean ACTUALLY is - what is it attempting to measure in everyday language??? It's extremely difficult to explain.

In fact, what the arithmetic mean is, goes something like: "If all the data were the same, but you had the same total as you had before, then the data value you get would be called the average". The aritmetic mean of 10, 20 30 is 20.

The geometric mean you get when you ask the same question for rates of interest (10%, 20% and 30% have a mean of 18.17%), and the harmonic mean you get when you ask the same question about speeds (10kmph, 20kmph, 30kmph have an mean of 16.3kmph) .

If anyone who was editing the average pages knew anything about descriptive statistics, this page should say something a lot different.

You certainly should not be reverting such pages, because you clearly don't have sufficient mathematical understanding to appreciate the nuances.

SeanTheSheep 03:05, 14 May 2007 (EDT)


The point about all of this is that calculations made on data sets are statistical estimates of something or other. If they are not, then there is no point to them. In this particular case, the average is an estimate of the central location or central tendency of the data, i.e. the answer to the question whereabouts is the data located?

A definition of average, which tells someone how to calculate one of the measures for this without explaining what we are trying to do, or discussing what the problems are in trying to capture such a thing is wrong.

The main reason that we almost uniformly use the arithmetic mean as the average is quite difficult to grasp: There is an important result in "Expectation Algebra" which says if you estimate the overall 'expected' mean of a probability distribution by using the arithmetic mean of a data set derived from that distribution, then the expected value of the distribution of arithmetic means is the mean that you started with; i.e. that the arithmetic mean is an unbiased estimator of the distribution mean (it is also a consistent estimator, and, as it turns out the most efficient estimator). Those are the reasons it is used, and that result underpins what is probably the most important theorem in the whole of statistics: The Central Limit Theorem.

However, I am not suggesting that we clutter up the definition with all of that. What I am saying though is that there are lots of different ways of trying to find the middle of a set of data, and that saying that average is (add them up and divide by the number of numbers) is inapproprate on three counts:

  • firstly that it ignores what the idea of average is trying to do,
  • secondly that it does not discuss whether "average" defined in this manner actually captures the required notion
  • thirdly it does not discuss in what situations an arithmetic average is, or is not appropriate.

--SeanTheSheep 04:31, 14 May 2007 (EDT)

Conservapedia is partially intended as a learning resource for homeschooled teenagers. An article like average should cover the topic clearly and concisely at a high school level before moving on to more advanced issues, and it should do so in simple language. You might want to try out writing drafts of more advanced material here. You certainly shouldn't replace something that's accurate and succinct with something that's richer and more advanced but harder to understand.
Averages have other uses besides being estimators of the mean of a normally distributed population. The arithmetic mean is very suitable for some of them. For example, if I drive 20,000 miles a year, and if I am trying to decide whether to buy a 50 mpg Prius or a 25 mpg PT Cruiser, the datum of interest to me in estimating fuel costs is the average (arithmetic mean) price of gas over the time period of interest... not the median or the mode or the kurtosis.
On the other hand... a Prius has a dashboard display that displays the average miles per gallon as a bar chart, over five-minute intervals. On a 25-minute trip, the display registers 30 mpg for the first five minutes, 35 mpg for the next five, 40 mpg for the next five, 45 mpg for the next five, 50 mpg for last five. Assuming the car is driven at a constant speed, what's the average mileage for the trip? Answer: the harmonic mean of 30, 35, 40, 45, and 50 = 38.72 mpg. I wouldn't call that practical, but it's one of the very few real-world examples I've ever come across where the right answer is the harmonic mean. (Another is the average speed of a consisting of equal distances driven at varying speeds... e.g. if I commute to work at an average speed of 70 mph and commute home at an average speed of 30 mph, what's my average speed for the day? Answer: the harmonic mean of 70 and 30. Dpbsmith 21:08, 14 May 2007 (EDT)
Not sure what you meant, Sean, and anyway your decision to skip a spell check doesn't raise my confidence in you. Nor does your attempt to use my editorial decision as a launching ground for an attack on the project. What did you even come here for?
If you're still around, read what I posted at talk:Median and what I added to Mean. I think I know more math than you: I have taught SAT prep (my math SAT, if you are familiar with US college placement tests, was 760 - that's in the 99th percentile, okay?).

some random math stuff in case anyone wants to use it

x_{avg} = \frac{x_1 + x_2 + x_3 + ... + x_n}{n}

Human 17:13, 14 May 2007 (EDT)

Analog for Average

Thanks for this, it makes the function of the arithmetic mean a LOT clearer, however, this does still not address the main problem here. AVERAGE is a conversational term used by people to indicate the centrality of data, and that can be measured in lots of ways. The arithmetic mean is only one of those averages, and as such, we should be indicating what the others are, and whether they measure up to the idea of "average".

AVERAGE is NOT Arithmetical mean.

--SeanTheSheep 03:48, 15 May 2007 (EDT)


See for example the following from http://www.yourdictionary.com/ahd/a/a0545300.html

definition n. Mathematics

  • A number that typifies a set of numbers of which it is a function.
  • See arithmetic mean.
  • An intermediate level or degree: near the average in size.
  • The usual or ordinary kind or quality: Although the wines vary, the average is quite good.
  • Sports The ratio of a team's or player's successful performances such as wins, hits, or goals, divided by total opportunities for successful performance, such as games, times at bat, or shots: finished the season with a .500 average; a batting average of .274.
  • Law: The loss of a ship or cargo, caused by damage at sea; The incurrence of damage or loss of a ship or cargo at sea; The equitable distribution of such a loss among concerned parties; . A charge incurred through such a loss.
  • Nautical Small expenses or charges that are usually paid by the master of a ship.

adj.

  • Mathematics Of, relating to, or constituting an average.
  • Being intermediate between extremes, as on a scale: a player of average ability.
  • Usual or ordinary in kind or character: a poll of average people; average eyesight.
  • Assessed in accordance with the law of averages.
  • Synonyms: average, medium, mediocre, fair1, middling, indifferent, tolerable; These adjectives indicate a middle position on a scale of evaluation. Average and medium apply to what is midway between extremes and imply both sufficiency and lack of distinction: a novel of average merit; an orange of medium size.
  • Mediocre stresses the undistinguished aspect of what is average: "The caliber of the students . . . has gone from mediocre to above average" (Judy Pasternak).
  • What is fair is passable but substantially below excellent: in fair health; Middling refers to a ranking between average and mediocre: gave a middling performance.
  • Indifferent suggests neutrality: "His home, alas, was but an indifferent attic" (Edward Everett Hale).
  • Something tolerable is merely acceptable: prepared a tolerable meal

--SeanTheSheep 03:55, 15 May 2007 (EDT)

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