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>
- quartiles