Editing Five-number summary (section)

==Example==
This example calculates the five-number summary for the following set of observations: 0, 0, 1, 2, 63, 61, 27, 13.
These are the number of moons of each planet in the [[Solar System]].

It helps to put the observations in ascending order: 0, 0, 1, 2, 13, 27, 61, 63. There are eight observations, so the median is the mean of the two middle numbers, (2 + 13)/2 = 7.5. Splitting the observations either side of the median gives two groups of four observations. The median of the first group is the lower or first quartile, and is equal to (0 + 1)/2 = 0.5. The median of the second group is the upper or third quartile, and is equal to (27 + 61)/2 = 44.
The smallest and largest observations are 0 and 63.

So the five-number summary would be 0, 0.5, 7.5, 44, 63.

===Example in R===
It is possible to calculate the five-number summary in the [[R programming language]] using the <code>fivenum</code> function. The <code>summary</code> function, when applied to a vector, displays the five-number summary together with the mean (which is not itself a part of the five-number summary). The <code>fivenum</code> uses a different method to calculate percentiles than the <code>summary</code> function.
{{sxhl|2=rout|
> moons <- c(0, 0, 1, 2, 63, 61, 27, 13)
> fivenum(moons)
[1]  0.0  0.5  7.5 44.0 63.0
> summary(moons)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   0.00    0.75    7.50   20.88   35.50   63.00 
}}

===Example in Python===
This python example uses the <code>percentile</code> function from the numerical library <code>numpy</code> and works in Python 2 and 3. 
<syntaxhighlight lang="numpy">
import numpy as np

def fivenum(data):
    """Five-number summary."""
    return np.percentile(data, [0, 25, 50, 75, 100], method="midpoint")
</syntaxhighlight>
<syntaxhighlight lang="pycon">
>>> moons = [0, 0, 1, 2, 63, 61, 27, 13]
>>> print(fivenum(moons))
[  0.    0.5   7.5  44.   63. ]
</syntaxhighlight>

=== Example in SAS ===
You can use <code>PROC UNIVARIATE</code> in [[SAS (software)|SAS]] to get the five number summary:
<syntaxhighlight lang="sas">
data fivenum;
input x @@;
datalines;
1 2 3 4 20 202 392 4 38 20
;
run;

ods select Quantiles;
proc univariate data = fivenum;
 output out = fivenums min = min Q1 = Q1 Q2 = median Q3 = Q3 max = max;
run;

proc print data = fivenums;
run;
</syntaxhighlight>

=== Example in Stata ===
[[File:Five number summary.png|thumb|336px|A five number summary of a distribution of data.]]
<syntaxhighlight lang="stata">
input byte y
0 
0 
1 
2 
63 
61 
27 
13
end 
list

tabstat y, statistics (min q max)
</syntaxhighlight>