woodiewo...@yahoo.com writes:
> On Tuesday, May 28, 2013 9:45:31 PM UTC-7, Lewis wrote:
>> In message <
d5094c61...@googlegroups.com>
>
> [...]
>
>> Think of how stupid the average person is, and realize half of them are
>> stupider than that.
>
> Sorry, I can't let that one pass. It tends to perpetuate a common
> misunderstanding about the meaning of "average". Half of people
> would be stupider than the median stupid person, but the word
> "average" usually refers to the mean, not the median.
>
> For example, consider the definition of "arithmetic mean" in an American Heritage Dictionary:
>
> ar·ith·met·ic mean
> n.
> The value obtained by dividing the sum of a set of quantities by the
> number of quantities in the set. Also called _average_.
>
> Consider the set of numbers [1,2,3,4,5,25]. The mean of the
> numbers, commonly called the average, is approximately 6.6667. Only
> one value is more than that, while five are less. But the median of
> the numbers is 3.5, because half are less than that and half are
> more.
>
> True, I've used a lopsided set to emphasize my point, but it's
> generally to be expected that any real-world distribution will have
> different median and mean.
Different, but typically not terribly so. A lot of data is normally
distributed, or nearly so, which means that the mean and median will
be very close. Since most of the mass of a normal distribution is
very near the mean, even a reasonably large perturbation isn't going
to move the median all that much. Where things aren't simply normally
distributed, they are often interpretable as the sum of two or more
normal distributions.
For example, looking at the data at
http://www.census.gov/compendia/statab/2012/tables/12s0209.pdf
the mean height for 30-39-year-old men in the US was 69.5 inches,
while the median was about 69.6. It's only when you average together
populations that you expect to systemmatically differ (such as men and
women or adults and children) that you expect to see large
differences.
> You could more truthfully say:
>
> Think of how stupid the median person is, and realize half of
> them are stupider than that.
IQ testing is predicated on the notion that you can model intelligence
by a normal distribution. For the SAT math test last year (for
college-bound seniors), the mean score was 514 and the median was
513. For Critical reading, the mean was 496 and the median was 497.
(To the precision I can tell from their tables.)
--
Evan Kirshenbaum +------------------------------------
Still with HP Labs |If to "man" a phone implies handing
SF Bay Area (1982-) |it over to a person of the male
Chicago (1964-1982) |gender, then to "monitor" it
|suggests handing it over to a
evan.kir...@gmail.com |lizard.
| Rohan Oberoi
http://www.kirshenbaum.net/