The mean and standard deviation are good descriptions of data from a nearly normal distribution, the five number summary is better for data from a skewed or fat-tails distribution.
Moore and McCabe in Section 1.2 of Introduction to the Practice of Statistics say "The five-number summary is usually better than the mean and standard deviation for describing a skewed distribution or a distribution with strong outliers. Use x-bar and s only for reasonably symmetric distributions that are free of outliers." On Wednesday, May 7, 2014, 'Bo Jacoby' via Programming < [email protected]> wrote: > What is the use of the Five Number Summary? If there are only a few > numbers, just list them. If there are plenty of numbers then the minimum > number and maximum number give little information. The better way of > summarizing a lot of numbers is to provide the mean value and the standard > deviation, I think. > M=.+/%# NB. Mean value > R=.M&.:*: NB. Root mean square > D=.-M NB. Deviation from mean > S=.R@D NB. Standard deviation > A=.M,.S NB. Arithmetic mean and standard deviation > G=.A&.:^. NB. Geometric mean and standard deviation > Thanks. Bo. > > > Den 8:18 onsdag den 7. maj 2014 skrev Linda Alvord < > [email protected] <javascript:;>>: > > Hopefully this will be more readable. I tried to write something that high > >school students could understand: > > > >A=:6 9 3 1 > > B=:6 9 3 1 4 > > l=: 13 :'(i.<.-:#y){/:~y' > > r=: 13 :'(i.<.-:#y){|./:~y' > > > > me=: 13 :'-:+/((<.,>.)-:<:#y){/:~y' > > > > (<./;([:me l);me;([: me r);>./)A > >--T-T---T---T-┐ > >│1│2│4.5│7.5│9│ > >L-+-+---+---+-- > > > > (<./;([:me l);me;([: me r);>./)B > >--T-T-T---T-┐ > >│1│2│4│7.5│9│ > >L-+-+-+---+-- > > > >Now I'll look at your other answers and see if I can simplify it even > more. > > > >Linda > > > >-----Original Message----- > >From: [email protected] > >[mailto:[email protected]] On Behalf Of Linda > Alvord > >Sent: Tuesday, May 06, 2014 5:39 PM > >To: [email protected] > >Subject: Re: [Jprogramming] Five Number Summary > > > >Kip, I get the same result as Raul. No need to load 'stats'. My new mean > >does not include @ . > > > > > > > >l=: 13 :'(i.<.-:#y){y' > >r=: 13 :'|.(i.<.-:#y){|.y' > > > >me=: 13 :'-:+/((<.,>.)-:<:#y){/:~y' > >(<./;([:me l);me;([: me r);>./)1 2 2 4 6 > >--T---T-T-T-┐ > >│1│1.5│2│5│6│ > >L-+---+-+-+-- > > > >I'm happy because the definition is all forks. > > > >5!:4 <'me' > >-- [: > >+- -: > >│ -- [: > >│ +- / --- + > >--+ │ -- [: > >│ │ │ -- <. > >│ │ +----+- , > >L----+ │ L- >. > >│ ------+ > >│ │ │ -- [: > >│ │ │ +- -: > >│ │ L----+ -- [: > >L-----+ L----+- <: > >│ L- # > >+- { > >L- ~ --- /: > > > > > >It looks better in J ! > > > >Linda > > > >-----Original Message----- > >From: [email protected] > >[mailto:[email protected]] On Behalf Of Kip Murray > >Sent: Tuesday, May 06, 2014 5:15 PM > >To: [email protected] > >Subject: Re: [Jprogramming] Five Number Summary > > > >Tukey used the name "fourths" because they are a little different from > >quartiles. > > > >On Tuesday, May 6, 2014, Joe Bogner <[email protected]> wrote: > > > >> On Tue, May 6, 2014 at 4:33 PM, Kip Murray > ><[email protected]<javascript:;>> > >> wrote: > >> > >> > jtfns 1 2 2 4 6 NB. correct > >> > 1 1.5 2 5 6 > >> > five 1 2 2 4 6 NB. doesn't work if repetitions in data > >> > 1 1 2 5 6 > >> > > >> > > >> On Tue, May 6, 2014 at 4:33 PM, Kip Murray > ><[email protected]<javascript:;>> > >> wrote: > >> > >> > five 1 2 2 4 6 NB. doesn't work if repetitions in data > >> > 1 1 2 5 6 > >> > > >> > > >> It's interesting that R gives even a different result ( > >> http://en.wikipedia.org/wiki/Five-number_summary#Example_in_R) > >> > >> > z <- c(1,2,2,4,6) > >> > fivenum(z) > >> [1] 1 2 2 4 6 > >> > summary(z) > >> Min. 1st Qu. Median Mean 3rd Qu. Max. > >> 1 2 2 3 4 6 > >> > >> > >> For the 1st quartile, Excel gives 2 with QUARTILE.INC and 1.5 > >> with QUARTILE.EXC > >> For the 3rd, Excel gives 4 an -- Sent from Gmail Mobile ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
