How Average is Average?

  laurie53 19:54 19 Sep 2007
Locked

Earlier today I read a report on computers in a consumer magazine.

It said that Dell was the only manufacturer to come out above average, and no brands were considered below average (there were 10 reported on).

Pardon?

I'm only a dumb old engineer so could any mathematician or statistician out there explain that to me in words of one syllable please?

  Stuartli 19:59 19 Sep 2007

There must be a benchmark of some sort on which to to base the below average, average and above average criteria.

Were any guidelines published with regard to a benchmark or overall assessment method?

  Pesala 20:04 19 Sep 2007

"The pure and simple truth is rarely pure and never simple."
Oscar Wilde

"First get your facts; then you can distort them at your leisure."
Mark Twain

  amonra 20:06 19 Sep 2007

If you sleep with your feet in the freezer and your head in the oven, then your body temperature will be average !

  Wilham 20:19 19 Sep 2007

laurie53: It's rubbish.

In any set of measurements, if Dell is sole manufacturer above the mean then there is at least one below it.

  Wilham 20:23 19 Sep 2007

"... at least one below the mean" of course.

Mean = Average

  justme 21:02 19 Sep 2007

Who said that the average was just the average of those computers in the article?

Consider this, if the average height of an adult male in Britain is ,say, 5 foot and 10 inches then it is possible to have a group of 10 people where 9 of them are an average height and 1 (at 6 foot) is above average.

Returning to your posting, it is possible that 9 computers were considered as average and only 1 was considered above average.

  Wilham 21:42 19 Sep 2007

justme: True, but you define what average you are talking about, "...average height of an adult male in Britain."
Without that it's meaningless.

  skeletal 22:13 19 Sep 2007

Wilham, you are correct. You must define the population before you can comment on its statistics.

laurie53’s first post does not mention population, therefore the reader assumes it is limited to the test (or at least I would!). Thus the statement about the mean is incorrect. Indeed, from the information, there are nine computers below average, and one (Dell) above.

(Consider nine computer each with a score of 5, and the Dell with a score of 6. The mean of these numbers is 5.1, therefore the score of 5 is below the mean.)

Skeletal

  Bapou 22:48 19 Sep 2007

In mathematics, an average, or central tendency of a data set refers to a measure of the "middle" or "expected" value of the data set. There are many different descriptive statistics that can be chosen as a measurement of the central tendency. The most common method is the arithmetic mean, but there are more than one type of average (median being another common example). Colloquially, people often use the term average to refer to an intuitive central tendency without having a specific measurement of central tendency in mind.
Wikipedia.

So there!

  UncleP 23:12 19 Sep 2007

laurie53 did not supply a link to the original article, so the problem may be that the comparison was not quantitative. That is, that the reviewer's opinion was that (in his experience) Dell was the best of the bunch and the rest were ok but not exceptional ie average. Or he might have been a little more subtle in implying that they were 'not below average' but actually 'pretty average' - without offending anybody, of course.

If a quantitative measure of performance was derived for each manufacturer, then the statement quoted by laurie53 implies that the reviewer had access to the statistics for this measure in the general population of manufacturers, against which to compare his sample. But of course all of this information should have been included in the article, to avoid confusion.

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