Re: How to test whether a number is harmony with a given set or not?

On 28 May 2006 19:30:58 -0700, "Sticker" <sticker.ji@xxxxxxxxx> wrote:

Not quite follow you how to get
Set one, in order, is (0, 5, 8, 9, 10, 55)
- Here's one cheap estimate of percentiles,
taking i/(k+1) -- (14, 29, 43, 57, 71, 86) .

Set two, in order, is (14, 19, 25, 67, 90)
with percentiles of (17, 33, 50, 67, 83) .

Now, re-write the values for Set one, so that
the overlapping numbers represent "tails"
- (0, 5, 8, 9, 10, 55) becomes
(86, 71, 57, 43, 29, 14)

explain to me will You?

Uh-oh. I'm not sure where you have a problem.
Sorting the data into order is straightforward, and
listing the two sets (use fixed-font for spacing),

Sets of scores:
one, (0, 5, 8, 9, 10, 55)
two, (14, 19, 25, 67, 90)

I'm thinking of the picture of two normal curves,
with overlapping "tails" -- For the second curve,
you can write out the Cumulative Distribution Function
in order to describe the fraction of scores that are
lower than any score, the "left" tail. For the first
curve, the "right" tail is described by one minus the
CDF. If you have not seen similar curves, then you
need to browse some more statistics.

_ _
/ \ / \
/ \/ \
/ /\ \



For data with 6 points, I estimated the percentiles
as the fractions that are 7ths, and similarly, used
6ths for the data with 5 points.

Percentiles as tail proportions for overlap.
(.86, .71, .57, .43, .29, .14)
(.17, .33, .50, .67, .83)


Hope this shows it.

--
Rich Ulrich, wpilib@xxxxxxxx
http://www.pitt.edu/~wpilib/index.html
.