Re: quartiles

*To*: mathgroup at smc.vnet.net*Subject*: [mg18232] Re: [mg18214] quartiles*From*: "Wolf, Hartmut" <hwolf at debis.com>*Date*: Thu, 24 Jun 1999 14:24:16 -0400*Organization*: debis Systemhaus*References*: <199906230041.UAA04362@smc.vnet.net.>*Sender*: owner-wri-mathgroup at wolfram.com

Hello Tom, Tom De Vries schrieb: > > Hello ! > > I am working with some statistics problems and have a question about finding > quartiles for a set of data > > Load in the package > > Needs["Statistics`DescriptiveStatistics`"] > > create a set of data > > salaries = > {250000,100000,60000,60000,40000,40000,40000,40000,25000,20000,20000,20000, > 18000,16000,16000} > > ask for the quartiles > > Quartiles[salaries] > > and this is the response > {20000,40000,55000} > > At this point I am probably revealing my ignorance of statistics.... > > 250000,100000,60000,60000,40000,40000, 40000 > 40000, Median > 25000,20000,20000,20000,18000,16000,16000 > > The lower quartile is the median of the values below the median, which I get > with Mathematica > 25000,20000,20000, > 20000, > 18000,16000,16000 > > The upper quartile should be the median of the numbers above the median, so > why is it 55000? > 250000,100000,60000, > 60000, > 40000,40000, 40000 > > Does Mathematica use some algorithm to get rid of outliers before finding > quartiles, or does it eliminate the median from the data set before finding > the quartiles, .....? > > The set of data I used as an example was taken from the math text I am using > and the answer the text supplies, and the answer I think I should get, is > different from the one Mathematica gets. I would appreciate any advice on this! > In[3]:= Needs["Statistics`DescriptiveStatistics`"] In[4]:= salaries = {250000,100000,60000,60000,40000,40000,40000,40000,25000, 20000,20000,20000,18000,16000,16000} In[5]:= Quartiles[salaries] Out[5]= {20000,40000,55000} How is this to be interpreted? Look at In[8]:= ?Quartiles "Quartiles[list] gives a list of the interpolated .25, .50, and .75 quantiles of the entries in list." Regard "interpolated". However if you do In[9]:= Quantile[salaries,#]&/@{1/4,1/2,3/4} Out[9]= {20000,40000,60000} which might be what you expect. But I think your definitions of lower and upper quartile are imprecise (what does "values below/above the median" mean exactly?) and sometimes incorrect. See: In[17]:= distr={1,1,1,2,3,3,3,3,3,3,4,4,4,4,4}; In[18]:= Quantile[distr,#]&/@{1/4,1/2,3/4} Out[18]= {2,3,4} But In[19]:= Median[With[{m=Median[distr]},Select[distr,#<m&]]] Out[19]= 1 In[20]:= Median[With[{m=Median[distr]},Select[distr,#>=m&]]] Out[20]= 3 kind regards, hw

**References**:**quartiles***From:*"Tom De Vries" <tdevries@shop.westworld.ca>