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Why is the 90th percentile of the following numbers 0.193204884?
0.193111065
0.188885706
0.191501273
0.193298704
0.18895934
0.192364606
How can the 90th percentile be greater than the greatest number in the set?
I used the formula - =PERCENTILE(R:R,0.9) on excel. [R:R is the excel range which contains the following numbers]
However, the 90th perentile of 1,2,3,4,5 comes out to be 4.6 which seems correct.

navneesi
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    $0.193298704$ is greater than $0.193204884$. – Lee Mosher Nov 15 '19 at 19:48
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    Thank you. Facepalm. I assumed that the numbers were in an ascending order without even looking at them. Have I always been this stupid or have I become stupid in the last couple of years? – navneesi Nov 15 '19 at 19:52
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    My brain has atrophied. My job very rarely requires me to think. It's just busywork. – navneesi Nov 15 '19 at 19:58
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    @navneesi: Maybe you need a different job! – Adrian Keister Nov 15 '19 at 21:19
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    New job or not, you should be aware that different texts and software programs use slightly different definitions of quantiles. For large samples, these differences are unimportant. – BruceET Nov 19 '19 at 09:00

1 Answers1

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Comment continued. R statistical software allows you to choose from among several different definitions of quantile, all widely used. [See documentation.]

set.seed(1119)
x = sort(round(rnorm(11, 50, 5)))
x
[1] 42 43 46 47 48 51 52 52 53 55 59

Here are results for quartiles using several different types.

quantile(x, type=4)
   0%   25%   50%   75%  100% 
42.00 45.25 49.50 52.25 59.00 

quantile(x, type=5)
   0%   25%   50%   75%  100% 
42.00 46.25 51.00 52.75 59.00 

quantile(x, type=6)
  0%  25%  50%  75% 100% 
  42   46   51   53   59

The idea is that some compromises are required when trying to partition eleven values into four appropriate groups; also the presence of ties can complicate finding quantiles. There is no universal agreement how best to do this. R uses type 7 as it's default.

quantile(x)  # if type unspecified, you get type 7
  0%  25%  50%  75% 100% 
42.0 46.5 51.0 52.5 59.0

So don't be surprised of you encounter discrepancies between a textbook definition and a particular type of software.

BruceET
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