25th and 75th percentile according to wolfram alpha

Question

I'm just studying my statistics exams and I came across something odd.

When I try to get the 25th or 75th percentile with wolfram alpha, it gives me another answer than I should get according to my textbooks.

simple example: http://www.wolframalpha.com/input/?i=first+quartile+32%2C42%2C46%2C46%2C54

according to my textbook, the answer should actually be 37 and not 39.5

Does anyone have any idea what wolfram alpha does different?

Related: http://stats.stackexchange.com/questions/10728/definition-of-quantile — Henry, Dec 13 '11 at 23:09

score 13 · Accepted Answer · edited Dec 14 '11 at 03:30

13

There are at least 9 [different definitions of empirical quantiles, see Wikipedia or the R manual (i.e., ? quantile). R computes the 25th percentile of your data as 37 if you specify type=6 (like Minitab and SPSS) and 39.5 if you specify type=5 (piecewise linear function):

> quantile(x=c(32,42,46,46,54), probs=0.25, type=5)
 25%
39.5
> quantile(x=c(32,42,46,46,54), probs=0.25, type=6)
 25%
37

edited Dec 14 '11 at 03:30

Jeromy Anglim

44,984

answered Dec 13 '11 at 20:58

psj

1,061

1

By default, R chooses type=7 to give a 25th percentile of 42 – Henry Aug 07 '20 at 08:32

25th and 75th percentile according to wolfram alpha

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