Centile

Question

Can anyone clear up a point for me (well my boss actually).

He says that Websters defines 99 centiles as the dividing points between 100 ordered and equal sets.
It is not clear how a point between the dividing lines should be described. Should a score of 99.7 be the 99th centile or the hundredth?
My take on this is that Websters seems to be saying that as 99 per cent of the population is below this mark, the percentile is 99.

In our mathematics competition we have never listed anyone as being in the 100th percentile - the highest has always been the 99th. Are we right? What should we say of a person who alone has the highest score? Are they at the 100th percentile?
Comments?

Richard Bollard
Canberra, Australia

Usenet · Accepted Answer

Richard Bollard filted:
[nq:1]Can anyone clear up a point for me (well my boss actually). He says that Websters defines 99 centiles as ... What should we say of a person who alone has the highest score? Are they at the 100th percentile? Comments?[/nq]
If there are 100 sets, and they are disjoint, there are 99 points at which one set is separated from another...(failure to take this into account is classified as a "fencepost" error)..
So if the centiles are defined as the dividing points, nobody is "on" one of them, but rather "at" the next lower one..
At the opposite end from the area that concerns you, this means that some must perforce score "below the first centile" or "at the zeroth centile"...as such people seldom nitpick over definitions, this difficulty is less often heard..r

Usenet · Answer

[nq:1]Can anyone clear up a point for me (well my boss actually). He says that Websters defines 99 centiles as the dividing points between 100 ordered and equal sets.[/nq]
Note: "Websters" is an empty term. In the words of the Merriam-Webster lawyers on their copyright pages: "The name /Webster/ alone is no guarantee of excellence. It is used by a number of publishers and mat serve mainly to mislead an unwary buyer."
The normal term is "percentile," although centile will do. "Centile" is used both for the 100 groups and for the 99 dividing lines between them. For example,
(COD10)
percentile /p@"sEntVIl/
· n. /Statistics/ each of the 100 equal groups into which a population can be divided according to the distribution of values of a particular variable.
Ø each of the 99 intermediate values of a random variable which divide a frequency distribution into 100 such groups.
Your boss is closer to the standard statistical use. "Websters" suggests a natural language use (e.g. COD10 definition above) rather than a term of art drawn from statistics.
The 19th CRC Standard Mathematical Tables defines percentile as: a) If the sample is arranged in ascending order of magnitude, the jth percentile P(j), j = 1, 2, ..., or 99 is given by the j*(n+1)/100th value. It may be necessary to interpolate between successive values.

The 31st CRC Standard Mathematical Tables and Formulae defines it by: Order statistics are obtained by arranging the sample values {x(1), ..., x(n)} in increasing order, denoted by
x(1) s, then s is above the 99th percentile mark (and is in the 100th percentile group). If you need finer gradations, then don't use percentiles.
[nq:1]My take on this is that Websters seems to be saying that as 99 per cent of the population is below this mark, the percentile is 99.[/nq]
The percentile group that this score is in has as its lower bound the 99th percentile mark (or simplu 99th percentile).
[nq:1]In our mathematics competition we have never listed anyone as being in the 100th percentile - the highest has always been the 99th. Are we right? What should we say of a person who alone has the highest score? Are they at the 100th percentile?[/nq]
If you have quantile marks Q(1)...Q(m), there must be scores x(i) below Q(1) and scores x(j) above Q(m). If you need finer gradations, don't use percentiles.

Usenet · Answer

[nq:1]Can anyone clear up a point for me (well my boss actually). He says that Websters defines 99 centiles as ... What should we say of a person who alone has the highest score? Are they at the 100th percentile? Comments?[/nq]
I would guess Martin Ambuhl's comprehensive post has pretty much fixed your wagon.
If you want to dazzle your boss on an international basis, you could mention the OED definition of percentile (which is equivalent, AFATAC, to centile):
a. adj. Pertaining to percentage; reckoned as a percentage. n. Each of a series of values obtained by dividing a large number of quantities into a hundred equal groups in order of magnitude; that value which is not exceeded by the lowest group is the first percentile; that not exceeded by the lowest two, the second percentile; and so on.

John Dean
Oxford

Usenet · Answer

[nq:2]Can anyone clear up a point for me (well my ... the highest score? Are they at the 100th percentile? Comments?[/nq]
[nq:1]I would guess Martin Ambuhl's comprehensive post has pretty much fixed your wagon. If you want to dazzle your boss ... the lowest group is the first percentile; that not exceeded by the lowest two, the second percentile; and so on.[/nq]
Thanks y'all. Comprehensive and clear as expected from this forum. (I told Herr Boss that I could get him some comprehensive analysis from this source to ease his troubled mind.)

Richard Bollard
Canberra, Australia

Usenet · Answer

[nq:1]Percentiles as described above (the CRC definition or the 2nd COD definition or your boss's version) are points on the ... the 99th percentile mark (and is in the 100th percentile group). If you need finer gradations, then don't use percentiles.[/nq]
milliles?
Jon Miller

Centile

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