Statistics function incorrectly computing median

[Ben Abbott]

On Jan 7, 2008, at 12:03 AM, Miguel Garcia-Blanco wrote:

>>>> What would the 1st quartile, median and 3rd quartile be for a
>>>> population of [0, 1, 2, 3, 4, 5]?
>>>>
>>>> My first impression would be 1.25, 2.5, and 3.75.
>
> I don't know about the quartiles, but 2.5 agrees with the only  
> definition I
> can find for sample median [1]. As for the population median, the
> distribution is symmetric so the median should coincide with the  
> population
> mean (mu = 2.5).

Regarding the median, it also agrees with the definition given by  
Wikipedia.

In probability theory and statistics, a median is described as the  
number separating the higher half of a sample, a population, or a  
probability distribution, from the lower half. The median of a finite  
list of numbers can be found by arranging all the observations from  
lowest value to highest value and picking the middle one. If there is  
an even number of observations, the median is not unique, so one often  
takes the mean of the two middle values.


> The statistical package R (GNU S) gives:
>> x <- c(0, 1, 2, 3, 4, 5)
>> quantile( x )
> 0%  25%  50%  75% 100%
> 0.00 1.25 2.50 3.75 5.00
>> summary( x )
>  Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
>  0.00    1.25    2.50    2.50    3.75    5.00
>
> [1] Equation (1) at http://mathworld.wolfram.com/StatisticalMedian.html 
>  (The
> same definition is also given in "John E. Freund's Mathematical  
> Statistics
> with Applications" by Miller and Miller.)
>
> -Miguel

I can duplicate those results by using a slightly different approach.  
However, I'd like to do some more tests. I don' t have R installed,  
nor am I familiar with using it.

Please see the attached file and compare my results to R .... and I'd  
like to see the results if they differ from mine.

Ben






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