Fivenum

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Revision as of 13:12, 15 March 2020 by SqrtNegInf (talk | contribs) (→‎{{header|Sidef}}: Fix link: Perl 6 --> Raku)
Fivenum is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Many big data or scientific programs use boxplots to show distributions of data.   In addition, sometimes saving large arrays for boxplots can be impractical and use extreme amounts of RAM.   It can be useful to save large arrays as arrays with five numbers to save memory.

For example, the   R   programming language implements Tukey's five-number summary as the fivenum function.


Task

Given an array of numbers, compute the five-number summary.


Note

While these five numbers can be used to draw a boxplot, statistical packages will typically need extra data. Moreover, while there is a consensus about the "box" of the boxplot, there are variations among statistical packages for the whiskers.

11l

Translation of: Python

<lang 11l>F fivenum(array) 

  V n = array.len
  V x = sorted(array)
  V n4 = floor((n + 3.0) / 2.0) / 2.0
  V d = [1.0, n4, (n + 1) / 2, n + 1 - n4, Float(n)]
  [Float] sum_array
  L(e) 5
     V fl = Int(floor(d[e] - 1))
     V ce = Int(ceil(d[e] - 1))
     sum_array.append(0.5 * (x[fl] + x[ce]))
  R sum_array

V x = [0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594, 0.73438555, -0.03035726, 1.46675970, 

     -0.74621349, -0.72588772, 0.63905160, 0.61501527, -0.98983780, -1.00447874, -0.62759469, 0.66206163,
      1.04312009, -0.10305385, 0.75775634, 0.32566578]

print(fivenum(x))</lang>

Output:
[-1.9506, -0.676741, 0.233247, 0.746071, 1.73132]

C

Translation of: Kotlin

<lang c>#include <stdio.h>

  1. include <stdlib.h>

double median(double *x, int start, int end_inclusive) { 

   int size = end_inclusive - start + 1;
   if (size <= 0) {
       printf("Array slice cannot be empty\n");
       exit(1);
   }
   int m = start + size / 2;
   if (size % 2) return x[m];
   return (x[m - 1] + x[m]) / 2.0;

}

int compare (const void *a, const void *b) { 

   double aa = *(double*)a; 
   double bb = *(double*)b;
   if (aa > bb) return 1;
   if (aa < bb) return -1;
   return 0;

}

int fivenum(double *x, double *result, int x_len) { 

   int i, m, lower_end;
   for (i = 0; i < x_len; i++) {
       if (x[i] != x[i]) {
          printf("Unable to deal with arrays containing NaN\n\n");
          return 1;
       }
   } 
   qsort(x, x_len, sizeof(double), compare);
   result[0] = x[0];
   result[2] = median(x, 0, x_len - 1);
   result[4] = x[x_len - 1];
   m = x_len / 2;
   lower_end = (x_len % 2) ? m : m - 1;
   result[1] = median(x, 0, lower_end);
   result[3] = median(x, m, x_len - 1);
   return 0;

}

int show(double *result, int places) { 

   int i;
   char f[7];
   sprintf(f, "%%.%dlf", places);
   printf("[");
   for (i = 0; i < 5; i++) {     
       printf(f, result[i]);
       if (i < 4) printf(", ");
   }
   printf("]\n\n");

}

int main() { 

   double result[5];

   double x1[11] = {15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0};
   if (!fivenum(x1, result, 11)) show(result, 1);

   double x2[6] = {36.0, 40.0, 7.0, 39.0, 41.0, 15.0};
   if (!fivenum(x2, result, 6)) show(result, 1);

   double x3[20] = {
        0.14082834,  0.09748790,  1.73131507,  0.87636009, -1.95059594,  0.73438555,
       -0.03035726,  1.46675970, -0.74621349, -0.72588772,  0.63905160,  0.61501527,
       -0.98983780, -1.00447874, -0.62759469,  0.66206163,  1.04312009, -0.10305385,
        0.75775634,  0.32566578
   };
   if (!fivenum(x3, result, 20)) show(result, 9);

   return 0;

}</lang>

Output:
[6.0, 25.5, 40.0, 42.5, 49.0]

[7.0, 15.0, 37.5, 40.0, 41.0]

[-1.950595940, -0.676741205, 0.233247060, 0.746070945, 1.731315070]

C#

Translation of: Java

<lang csharp>using System; using System.Collections.Generic; using System.Linq; using System.Text;

namespace Fivenum { 

   public static class Helper {
       public static string AsString<T>(this ICollection<T> c, string format = "{0}") {
           StringBuilder sb = new StringBuilder("[");
           int count = 0;
           foreach (var t in c) {
               if (count++ > 0) {
                   sb.Append(", ");
               }
               sb.AppendFormat(format, t);
           }
           return sb.Append("]").ToString();
       }
   }

   class Program {
       static double Median(double[] x, int start, int endInclusive) {
           int size = endInclusive - start + 1;
           if (size <= 0) throw new ArgumentException("Array slice cannot be empty");
           int m = start + size / 2;
           return (size % 2 == 1) ? x[m] : (x[m - 1] + x[m]) / 2.0;
       }

       static double[] Fivenum(double[] x) {
           foreach (var d in x) {
               if (Double.IsNaN(d)) {
                   throw new ArgumentException("Unable to deal with arrays containing NaN");
               }
           }
           double[] result = new double[5];
           Array.Sort(x);
           result[0] = x.First();
           result[2] = Median(x, 0, x.Length - 1);
           result[4] = x.Last();
           int m = x.Length / 2;
           int lowerEnd = (x.Length % 2 == 1) ? m : m - 1;
           result[1] = Median(x, 0, lowerEnd);
           result[3] = Median(x, m, x.Length - 1);
           return result;
       }

       static void Main(string[] args) {
           double[][] x1 = new double[][]{
               new double[]{ 15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0},
               new double[]{ 36.0, 40.0, 7.0, 39.0, 41.0, 15.0},
               new double[]{
                    0.14082834,  0.09748790,  1.73131507,  0.87636009, -1.95059594,  0.73438555,
                   -0.03035726,  1.46675970, -0.74621349, -0.72588772,  0.63905160,  0.61501527,
                   -0.98983780, -1.00447874, -0.62759469,  0.66206163,  1.04312009, -0.10305385,
                    0.75775634,  0.32566578
               },
           };
           foreach(var x in x1) {
               var result = Fivenum(x);
               Console.WriteLine(result.AsString("{0:F8}"));
           }
       }
   }

}</lang>

Output:
[6.00000000, 25.50000000, 40.00000000, 42.50000000, 49.00000000]
[7.00000000, 15.00000000, 37.50000000, 40.00000000, 41.00000000]
[-1.95059594, -0.67674121, 0.23324706, 0.74607095, 1.73131507]

C++

Translation of: D

<lang cpp>#include <algorithm>

  1. include <iostream>
  2. include <ostream>
  3. include <vector>

///////////////////////////////////////////////////////////////////////////// // The following is taken from https://cpplove.blogspot.com/2012/07/printing-tuples.html

// Define a type which holds an unsigned integer value template<std::size_t> struct int_ {};

template <class Tuple, size_t Pos> std::ostream& print_tuple(std::ostream& out, const Tuple& t, int_<Pos>) { 

   out << std::get< std::tuple_size<Tuple>::value - Pos >(t) << ", ";
   return print_tuple(out, t, int_<Pos - 1>());

}

template <class Tuple> std::ostream& print_tuple(std::ostream& out, const Tuple& t, int_<1>) { 

   return out << std::get<std::tuple_size<Tuple>::value - 1>(t);

}

template <class... Args> std::ostream& operator<<(std::ostream& out, const std::tuple<Args...>& t) { 

   out << '(';
   print_tuple(out, t, int_<sizeof...(Args)>());
   return out << ')';

}

/////////////////////////////////////////////////////////////////////////////

template <class RI> double median(RI beg, RI end) { 

   if (beg == end) throw std::runtime_error("Range cannot be empty");
   auto len = end - beg;
   auto m = len / 2;
   if (len % 2 == 1) {
       return *(beg + m);
   }

   return (beg[m - 1] + beg[m]) / 2.0;

}

template <class C> auto fivenum(C& c) { 

   std::sort(c.begin(), c.end());

   auto cbeg = c.cbegin();
   auto cend = c.cend();

   auto len = cend - cbeg;
   auto m = len / 2;
   auto lower = (len % 2 == 1) ? m : m - 1;
   double r2 = median(cbeg, cbeg + lower + 1);
   double r3 = median(cbeg, cend);
   double r4 = median(cbeg + lower + 1, cend);

   return std::make_tuple(*cbeg, r2, r3, r4, *(cend - 1));

}

int main() { 

   using namespace std;
   vector<vector<double>> cs = {
       { 15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0 },
       { 36.0, 40.0, 7.0, 39.0, 41.0, 15.0 },
       {
           0.14082834,  0.09748790,  1.73131507,  0.87636009, -1.95059594,  0.73438555,
          -0.03035726,  1.46675970, -0.74621349, -0.72588772,  0.63905160,  0.61501527,
          -0.98983780, -1.00447874, -0.62759469,  0.66206163,  1.04312009, -0.10305385,
           0.75775634,  0.32566578
       }
   };

   for (auto & c : cs) {
       cout << fivenum(c) << endl;
   }

   return 0;

}</lang>

Output:
(6, 25.5, 40, 43, 49)
(7, 15, 37.5, 40, 41)
(-1.9506, -0.676741, 0.233247, 0.746071, 1.73132)

D

Translation of: Java

<lang d>import std.algorithm; import std.exception; import std.math; import std.stdio;

double median(double[] x) { 

   enforce(x.length >= 0, "Array slice cannot be empty");
   int m = x.length / 2;
   if (x.length % 2 == 1) {
       return x[m];
   }
   return (x[m-1] + x[m]) / 2.0;

}

double[] fivenum(double[] x) { 

   foreach (d; x) {
       enforce(!d.isNaN, "Unable to deal with arrays containing NaN");
   }

   double[] result;
   result.length = 5;

   x.sort;
   result[0] = x[0];
   result[2] = median(x);
   result[4] = x[$-1];

   int m = x.length / 2;
   int lower = (x.length % 2 == 1) ? m : m - 1;
   result[1] = median(x[0..lower+1]);
   result[3] = median(x[lower+1..$]);

   return result;

}

void main() { 

   double[][] x1 = [
       [15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0],
       [36.0, 40.0, 7.0, 39.0, 41.0, 15.0],
       [
           0.14082834,  0.09748790,  1.73131507,  0.87636009, -1.95059594,  0.73438555,
          -0.03035726,  1.46675970, -0.74621349, -0.72588772,  0.63905160,  0.61501527,
          -0.98983780, -1.00447874, -0.62759469,  0.66206163,  1.04312009, -0.10305385,
           0.75775634,  0.32566578
       ]
   ];
   foreach(x; x1) {
       writeln(fivenum(x));
   }

}</lang>

Output:
[6, 25.5, 40, 43, 49]
[7, 15, 37.5, 40, 41]
[-1.9506, -0.676741, 0.233247, 0.746071, 1.73132]

F#

Translation of: C#

<lang fsharp>open System

// Take from https://stackoverflow.com/a/1175123 let rec last = function 

   | hd :: [] -> hd
   | _ :: tl -> last tl
   | _ -> failwith "Empty list."

let median x = 

   for e in x do
       if Double.IsNaN(e) then failwith "unable to deal with lists containing NaN"

   let size = List.length(x)
   if size <= 0 then failwith "Array slice cannot be empty"
   let m = size / 2
   if size % 2 = 1 then x.[m]
   else (x.[m - 1] + x.[m]) / 2.0

let fivenum x = 

   let x2 = List.sort(x)
   let m = List.length(x2) / 2
   let lowerEnd = if List.length(x2) % 2 = 1 then m else m - 1
   [List.head x2, median x2.[..lowerEnd], median x2, median x2.[m..], last x2]

[<EntryPoint>] let main _ = 

   let x1 = [
       [15.0; 6.0; 42.0; 41.0; 7.0; 36.0; 49.0; 40.0; 39.0; 47.0; 43.0];
       [36.0; 40.0; 7.0; 39.0; 41.0; 15.0];
       [
            0.14082834;  0.09748790;  1.73131507;  0.87636009; -1.95059594;
            0.73438555; -0.03035726;  1.46675970; -0.74621349; -0.72588772;
            0.63905160;  0.61501527; -0.98983780; -1.00447874; -0.62759469;
            0.66206163;  1.04312009; -0.10305385;  0.75775634;  0.32566578
       ]
   ]

   for a in x1 do
       let y = fivenum a
       Console.WriteLine("{0}", y);

   0 // return an integer exit code</lang>
Output:
[(6, 25.5, 40, 42.5, 49)]
[(7, 15, 37.5, 40, 41)]
[(-1.95059594, -0.676741205, 0.23324706, 0.746070945, 1.73131507)]

Factor

<lang factor>USING: combinators combinators.smart kernel math math.statistics prettyprint sequences sorting ; IN: rosetta-code.five-number

<PRIVATE

bisect ( seq -- lower upper )
   dup length even? [ halves ]
   [ dup midpoint@ 1 + [ head ] [ tail* ] 2bi ] if ;
(fivenum) ( seq -- summary )
   natural-sort {
       [ infimum ]
       [ bisect drop median ]
       [ median ]
       [ bisect nip median ]
       [ supremum ]
   } cleave>array ;

PRIVATE>

ERROR: fivenum-empty data ; ERROR: fivenum-nan data ;

fivenum ( seq -- summary )
   {
       { [ dup empty? ] [ fivenum-empty ] }
       { [ dup [ fp-nan? ] any? ] [ fivenum-nan ] }
       [ (fivenum) ]
   } cond ;
fivenum-demo ( -- )
   { 15 6 42 41 7 36 49 40 39 47 43 }
   { 36 40 7 39 41 15 }
   {  0.14082834  0.09748790  1.73131507  0.87636009
     -1.95059594  0.73438555 -0.03035726  1.46675970
     -0.74621349 -0.72588772  0.63905160  0.61501527
     -0.98983780 -1.00447874 -0.62759469  0.66206163
      1.04312009 -0.10305385  0.75775634  0.32566578 }
   [ fivenum . ] tri@ ;

MAIN: fivenum-demo</lang>

Output:
{ 6 25+1/2 40 42+1/2 49 }
{ 7 15 37+1/2 40 41 }
{ -1.95059594 -0.676741205 0.23324706 0.746070945 1.73131507 }

Go

Translation of: Perl

<lang go>package main

import ( 

   "fmt"
   "math"
   "sort"

)

func fivenum(a []float64) (n5 [5]float64) { 

   sort.Float64s(a)
   n := float64(len(a))
   n4 := float64((len(a)+3)/2) / 2
   d := []float64{1, n4, (n + 1) / 2, n + 1 - n4, n}
   for e, de := range d {
       floor := int(de - 1)
       ceil := int(math.Ceil(de - 1))
       n5[e] = .5 * (a[floor] + a[ceil])
   }
   return

}

var ( 

   x1 = []float64{36, 40, 7, 39, 41, 15}
   x2 = []float64{15, 6, 42, 41, 7, 36, 49, 40, 39, 47, 43}
   x3 = []float64{
       0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594,
       0.73438555, -0.03035726, 1.46675970, -0.74621349, -0.72588772,
       0.63905160, 0.61501527, -0.98983780, -1.00447874, -0.62759469,
       0.66206163, 1.04312009, -0.10305385, 0.75775634, 0.32566578,
   }

)

func main() { 

   fmt.Println(fivenum(x1))
   fmt.Println(fivenum(x2))
   fmt.Println(fivenum(x3))

}</lang>

Output:
[7 15 37.5 40 41]
[6 25.5 40 42.5 49]
[-1.95059594 -0.676741205 0.23324706 0.746070945 1.73131507]

Alternate:

This solution is aimed at handling larger data sets more efficiently. It replaces the O(n log n) sort with O(n) quickselect. It also does not attempt to reproduce the R result exactly, to average values to get a median of an even number of data values, or otherwise estimate quantiles. The quickselect here leaves the input partitioned around the selected value, which allows another small optimization: The first quickselect call partitions the full input around the median. The second call, to get the first quartile, thus only has to process the partition up to the median. The third call, to get the minimum, only has to process the partition up to the first quartile. The 3rd quartile and maximum are obtained similarly. <lang go>package main

import ( 

   "fmt"
   "math/rand"

)

func fivenum(a []float64) (n [5]float64) { 

   last := len(a) - 1
   m := last / 2
   n[2] = qsel(a, m)
   q1 := len(a) / 4
   n[1] = qsel(a[:m], q1)
   n[0] = qsel(a[:q1], 0)
   a = a[m:]
   q3 := last - m - q1
   n[3] = qsel(a, q3)
   a = a[q3:]
   n[4] = qsel(a, len(a)-1)
   return

}

func qsel(a []float64, k int) float64 { 

   for len(a) > 1 {
       px := rand.Intn(len(a))
       pv := a[px]
       last := len(a) - 1
       a[px], a[last] = a[last], pv
       px = 0
       for i, v := range a[:last] {
           if v < pv {
               a[px], a[i] = v, a[px]
               px++
           }
       }
       a[px], a[last] = pv, a[px]
       if px == k {
           return pv
       }
       if k < px {
           a = a[:px]
       } else {
           a = a[px+1:]
           k -= px + 1
       }
   }
   return a[0]

}

var ( 

   x1 = []float64{36, 40, 7, 39, 41, 15}
   x2 = []float64{15, 6, 42, 41, 7, 36, 49, 40, 39, 47, 43}
   x3 = []float64{
       0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594,
       0.73438555, -0.03035726, 1.46675970, -0.74621349, -0.72588772,
       0.63905160, 0.61501527, -0.98983780, -1.00447874, -0.62759469,
       0.66206163, 1.04312009, -0.10305385, 0.75775634, 0.32566578,
   }

)

func main() { 

   fmt.Println(fivenum(x1))
   fmt.Println(fivenum(x2))
   fmt.Println(fivenum(x3))

}</lang>

Output:
[7 15 36 40 41]
[6 15 40 43 49]
[-1.95059594 -0.62759469 0.14082834 0.73438555 1.73131507]

J

Solution <lang j>midpts=: (1 + #) <:@(] , -:@[ , -) -:@<.@-:@(3 + #) NB. mid points of y quartiles=: -:@(+/)@((<. ,: >.)@midpts { /:~@]) NB. quartiles of y fivenum=: <./ , quartiles , >./ NB. fivenum summary of y</lang> Example Usage <lang j> test1=: 15 6 42 41 7 36 49 40 39 47 43 

  test2=: 36 40 7 39 41 15
  test3=: , 0 ". ];._2 noun define
0.14082834  0.09748790  1.73131507  0.87636009 -1.95059594
0.73438555 -0.03035726  1.46675970 -0.74621349 -0.72588772
0.63905160  0.61501527 -0.98983780 -1.00447874 -0.62759469
0.66206163  1.04312009 -0.10305385  0.75775634  0.32566578

) 

  fivenum &> test1;test2;test3
     6      25.5       40     42.5      49
     7        15     37.5       40      41

_1.9506 _0.676741 0.233247 0.746071 1.73132</lang>

Java

Translation of: Kotlin

<lang java>import java.util.Arrays;

public class Fivenum { 

   static double median(double[] x, int start, int endInclusive) {
       int size = endInclusive - start + 1;
       if (size <= 0) throw new IllegalArgumentException("Array slice cannot be empty");
       int m = start + size / 2;
       return (size % 2 == 1) ? x[m] : (x[m - 1] + x[m]) / 2.0;
   }

   static double[] fivenum(double[] x) {
       for (Double d : x) {
           if (d.isNaN())
               throw new IllegalArgumentException("Unable to deal with arrays containing NaN");
       }
       double[] result = new double[5];
       Arrays.sort(x);
       result[0] = x[0];
       result[2] = median(x, 0, x.length - 1);
       result[4] = x[x.length - 1];
       int m = x.length / 2;
       int lowerEnd = (x.length % 2 == 1) ? m : m - 1;
       result[1] = median(x, 0, lowerEnd);
       result[3] = median(x, m, x.length - 1);
       return result;
   }

   public static void main(String[] args) {
       double xl[][] = {
           {15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0},
           {36.0, 40.0, 7.0, 39.0, 41.0, 15.0},
           {
                0.14082834,  0.09748790,  1.73131507,  0.87636009, -1.95059594,  0.73438555,
               -0.03035726,  1.46675970, -0.74621349, -0.72588772,  0.63905160,  0.61501527,
               -0.98983780, -1.00447874, -0.62759469,  0.66206163,  1.04312009, -0.10305385,
                0.75775634,  0.32566578
           }
       };
       for (double[] x : xl) System.out.printf("%s\n\n", Arrays.toString(fivenum(x)));
   }

}</lang>

Output:
[6.0, 25.5, 40.0, 42.5, 49.0]

[7.0, 15.0, 37.5, 40.0, 41.0]

[-1.95059594, -0.676741205, 0.23324706, 0.746070945, 1.73131507]

Julia

Works with: Julia version 0.6

<lang julia>function mediansorted(x::AbstractVector{T}, i::Integer, l::Integer)::T where T 

   len = l - i + 1
   len > zero(len) || throw(ArgumentError("Array slice cannot be empty."))
   mid = i + len ÷ 2
   return isodd(len) ? x[mid] : (x[mid-1] + x[mid]) / 2

end

function fivenum(x::AbstractVector{T}) where T<:AbstractFloat 

   r = Vector{T}(5)
   xs = sort(x)
   mid::Int = length(xs) ÷ 2
   lowerend::Int = isodd(length(xs)) ? mid : mid - 1
   r[1] = xs[1]
   r[2] = mediansorted(xs, 1, lowerend)
   r[3] = mediansorted(xs, 1, endof(xs))
   r[4] = mediansorted(xs, mid, endof(xs))
   r[end] = xs[end]
   return r

end

for v in ([15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0], 

         [36.0, 40.0, 7.0, 39.0, 41.0, 15.0],
         [0.14082834,  0.09748790,  1.73131507,  0.87636009, -1.95059594,  0.73438555,
         -0.03035726,  1.46675970, -0.74621349, -0.72588772,  0.63905160,  0.61501527,
         -0.98983780, -1.00447874, -0.62759469,  0.66206163,  1.04312009, -0.10305385,
          0.75775634,  0.32566578])
   println("# ", v, "\n -> ", fivenum(v))

end</lang>

Output:
# [15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0]
 -> [6.0, 15.0, 40.0, 42.0, 49.0]
# [36.0, 40.0, 7.0, 39.0, 41.0, 15.0]
 -> [7.0, 11.0, 37.5, 39.5, 41.0]
# [0.140828, 0.0974879, 1.73132, 0.87636, -1.9506, 0.734386, -0.0303573, 1.46676, -0.746213, -0.725888, 0.639052, 0.615015, -0.989838, -1.00448, -0.627595,0.662062, 1.04312, -0.103054, 0.757756, 0.325666]
 -> [-1.9506, -0.725888, 0.233247, 0.734386, 1.73132]

Kotlin

The following uses Tukey's method for calculating the lower and upper quartiles (or 'hinges') which is what the R function, fivenum, appears to use.

As arrays containing NaNs and nulls cannot really be dealt with in a sensible fashion in Kotlin, they've been excluded altogether. <lang scala>// version 1.2.21

fun median(x: DoubleArray, start: Int, endInclusive: Int): Double { 

   val size = endInclusive - start + 1
   require (size > 0) { "Array slice cannot be empty" }
   val m = start + size / 2
   return if (size % 2 == 1) x[m] else (x[m - 1] + x[m]) / 2.0

}

fun fivenum(x: DoubleArray): DoubleArray { 

   require(x.none { it.isNaN() }) { "Unable to deal with arrays containing NaN" }
   val result = DoubleArray(5)
   x.sort()
   result[0] = x[0]
   result[2] = median(x, 0, x.size - 1)
   result[4] = x[x.lastIndex]
   val m = x.size / 2
   var lowerEnd = if (x.size % 2 == 1) m else m - 1
   result[1] = median(x, 0, lowerEnd)
   result[3] = median(x, m, x.size - 1)
   return result

}

fun main(args: Array<String>) { 

   var xl = listOf(
       doubleArrayOf(15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0),
       doubleArrayOf(36.0, 40.0, 7.0, 39.0, 41.0, 15.0),
       doubleArrayOf(
            0.14082834,  0.09748790,  1.73131507,  0.87636009, -1.95059594,  0.73438555,
           -0.03035726,  1.46675970, -0.74621349, -0.72588772,  0.63905160,  0.61501527,
           -0.98983780, -1.00447874, -0.62759469,  0.66206163,  1.04312009, -0.10305385,
            0.75775634,  0.32566578
       )
   )
   xl.forEach { println("${fivenum(it).asList()}\n") }

}</lang>

Output:
[6.0, 25.5, 40.0, 42.5, 49.0]

[7.0, 15.0, 37.5, 40.0, 41.0]

[-1.95059594, -0.676741205, 0.23324706, 0.746070945, 1.73131507]

Lua

<lang lua>function slice(tbl, low, high) 

   local copy = {}

   for i=low or 1, high or #tbl do
       copy[#copy+1] = tbl[i]
   end

   return copy

end

-- assumes that tbl is sorted function median(tbl) 

   m = math.floor(#tbl / 2) + 1
   if #tbl % 2 == 1 then
       return tbl[m]
   end
   return (tbl[m-1] + tbl[m]) / 2

end

function fivenum(tbl) 

   table.sort(tbl)

   r0 = tbl[1]
   r2 = median(tbl)
   r4 = tbl[#tbl]

   m = math.floor(#tbl / 2)
   if #tbl % 2 == 1 then
       low = m
   else
       low = m - 1
   end
   r1 = median(slice(tbl, nil, low+1))
   r3 = median(slice(tbl, low+2, nil))

   return r0, r1, r2, r3, r4

end

x1 = { 

   {15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0},
   {36.0, 40.0, 7.0, 39.0, 41.0, 15.0},
   {
       0.14082834,  0.09748790,  1.73131507,  0.87636009, -1.95059594,  0.73438555,
      -0.03035726,  1.46675970, -0.74621349, -0.72588772,  0.63905160,  0.61501527,
      -0.98983780, -1.00447874, -0.62759469,  0.66206163,  1.04312009, -0.10305385,
       0.75775634,  0.32566578
   }

}

for i,x in ipairs(x1) do 

   print(fivenum(x))

end</lang>

Output:
6       25.5    40      43      49
7       15      37.5    40      41
-1.95059594     -0.676741205    0.23324706      0.746070945     1.73131507

Modula-2

<lang modula2>MODULE Fivenum; FROM FormatString IMPORT FormatString; FROM LongStr IMPORT RealToStr; FROM Terminal IMPORT WriteString,WriteLn,ReadChar;

PROCEDURE WriteLongReal(v : LONGREAL); VAR buf : ARRAY[0..63] OF CHAR; BEGIN 

   RealToStr(v, buf);
   WriteString(buf)

END WriteLongReal;

PROCEDURE WriteArray(arr : ARRAY OF LONGREAL); VAR i : CARDINAL; BEGIN 

   WriteString("[");
   FOR i:=0 TO HIGH(arr) DO
       WriteLongReal(arr[i]);
       WriteString(", ")
   END;
   WriteString("]")

END WriteArray;

(* Assumes that the input is sorted *) PROCEDURE Median(x : ARRAY OF LONGREAL; beg,end : CARDINAL) : LONGREAL; VAR m,cnt : CARDINAL; BEGIN 

   cnt := end - beg + 1;
   m := cnt / 2;
   IF cnt MOD 2 = 1 THEN
       RETURN x[beg + m]
   END;
   RETURN (x[beg + m - 1] + x[beg + m]) / 2.0

END Median;

TYPE Summary = ARRAY[0..4] OF LONGREAL; PROCEDURE Fivenum(input : ARRAY OF LONGREAL) : Summary; 

   PROCEDURE Sort();
   VAR
       i,j : CARDINAL;
       t : LONGREAL;
   BEGIN
       FOR i:=0 TO HIGH(input) DO
           FOR j:=0 TO HIGH(input) DO
               IF (i#j) AND (input[i] < input[j]) THEN
                   t := input[i];
                   input[i] := input[j];
                   input[j] := t
               END
           END
       END
   END Sort;

VAR 

   result : Summary;
   size,m,low : CARDINAL;

BEGIN 

   size := HIGH(input);
   Sort();

   result[0] := input[0];
   result[2] := Median(input,0,size);
   result[4] := input[size];

   m := size / 2;
   IF (size MOD 2 = 1) THEN
       low := m
   ELSE
       low := m - 1
   END;
   result[1] := Median(input, 0, m);
   result[3] := Median(input, m+1, size);

   RETURN result;

END Fivenum;

TYPE 

   A6 = ARRAY[0..5] OF LONGREAL;
   A11 = ARRAY[0..10] OF LONGREAL;
   A20 = ARRAY[0..19] OF LONGREAL;

VAR 

   a6 : A6;
   a11 : A11;
   a20 : A20;

BEGIN 

   a11 := A11{15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0};
   WriteArray(Fivenum(a11));
   WriteLn;
   WriteLn;

   a6 := A6{36.0, 40.0, 7.0, 39.0, 41.0, 15.0};
   WriteArray(Fivenum(a6));
   WriteLn;
   WriteLn;

   a20 := A20{
       0.14082834,  0.09748790,  1.73131507,  0.87636009, -1.95059594,  0.73438555,
       -0.03035726,  1.46675970, -0.74621349, -0.72588772,  0.63905160,  0.61501527,
       -0.98983780, -1.00447874, -0.62759469,  0.66206163,  1.04312009, -0.10305385,
       0.75775634,  0.32566578
   };
   WriteArray(Fivenum(a20));
   WriteLn;

   ReadChar

END Fivenum.</lang>

Output:
[6.000000000000000, 25.499999999999900, 40.000000000000000, 42.499999999999900, 49.000000000000000, ]

[7.000000000000000, 15.000000000000000, 35.500000000000000, 40.000000000000000, 40.499999999999900, ]

[-1.950594000000000, -0.676741205000000, 0.233247060000000, 0.746070945000000, 1.731315070000000, ]

Perl

<lang Perl>use POSIX qw(ceil floor);

sub fivenum { 

  my(@array) = @_;
  my $n = scalar @array;
  die "No values were entered into fivenum!" if $n == 0;
  my @x = sort {$a <=> $b} @array;
  my $n4 = floor(($n+3)/2)/2;
  my @d = (1, $n4, ($n +1)/2, $n+1-$n4, $n);
  my @sum_array;
  for my $e (0..4) {
     my $floor = floor($d[$e]-1);
     my $ceil  =  ceil($d[$e]-1);
     push @sum_array, (0.5 * ($x[$floor] + $x[$ceil]));
  }
  return @sum_array;

}

my @x = (15, 6, 42, 41, 7, 36, 49, 40, 39, 47, 43); my @tukey = fivenum(\@x); say join (',', @tukey);

  1. ----------

@x = (36, 40, 7, 39, 41, 15), @tukey = fivenum(\@x); say join (',', @tukey);

  1. ----------

@x = (0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594, 

    0.73438555, -0.03035726,  1.46675970, -0.74621349, -0.72588772,
    0.63905160,  0.61501527, -0.98983780, -1.00447874, -0.62759469,
    0.66206163,  1.04312009, -0.10305385,  0.75775634,  0.32566578);

@tukey = fivenum(\@x); say join (',', @tukey);</lang>

Output:
6,25.5,40,42.5,49
7,15,37.5,40,41
-1.95059594,-0.676741205,0.23324706,0.746070945,1.73131507

Phix

<lang Phix>function median(sequence tbl, integer lo, hi) 

   integer l = hi-lo+1
   integer m = lo+floor(l/2)
   if remainder(l,2)=1 then
       return tbl[m]
   end if
   return (tbl[m-1]+tbl[m])/2

end function

function fivenum(sequence tbl) 

   tbl = sort(tbl)
   integer l = length(tbl),
           m = floor(l/2)+remainder(l,2)

   atom r1 = tbl[1],
        r2 = median(tbl,1,m),
        r3 = median(tbl,1,l),
        r4 = median(tbl,m+1,l),
        r5 = tbl[l]

   return {r1, r2, r3, r4, r5}

end function

constant x1 = {15, 6, 42, 41, 7, 36, 49, 40, 39, 47, 43}, 

        x2 = {36, 40, 7, 39, 41, 15},
        x3 = {0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594,
              0.73438555, -0.03035726, 1.46675970, -0.74621349, -0.72588772,
              0.63905160, 0.61501527, -0.98983780, -1.00447874, -0.62759469,
              0.66206163, 1.04312009, -0.10305385, 0.75775634, 0.32566578}

?fivenum(x1) ?fivenum(x2) ?fivenum(x3)</lang>

Output:
{6,25.5,40,43,49}
{7,15,37.5,40,41}
{-1.95059594,-0.676741205,0.23324706,0.746070945,1.73131507}

Python

Python: Standard commands

Translation of: Perl

Work with: Python 2

Work with: Python 3 <lang python>from __future__ import division import math import sys

def fivenum(array): 

   n = len(array)
   if n == 0:
       print("you entered an empty array.")
       sys.exit()
   x = sorted(array)
   
   n4 = math.floor((n+3.0)/2.0)/2.0
   d = [1, n4, (n+1)/2, n+1-n4, n]
   sum_array = []
   
   for e in range(5):
       floor = int(math.floor(d[e] - 1))
       ceil = int(math.ceil(d[e] - 1))
       sum_array.append(0.5 * (x[floor] + x[ceil]))
   
   return sum_array

x = [0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594, 0.73438555, -0.03035726, 1.46675970, -0.74621349, -0.72588772, 0.63905160, 0.61501527, -0.98983780, -1.00447874, -0.62759469, 0.66206163, 1.04312009, -0.10305385, 0.75775634, 0.32566578]

y = fivenum(x) print(y)</lang>

Output:
[-1.95059594, -0.676741205, 0.23324706, 0.746070945, 1.73131507]

Python: Pandas library

There are many ways to compute this kind of summary statistics (see wp:Percentile#Definitions). The Python Pandas library supports a range.

Pandas is a well known Python library. Its Dataframe.describe method produces summary stats from data.

(Though these 25% and 75% values do not correspond to the Fivenum Tukey quartile values specified in this task) <lang python>import pandas as pd pd.DataFrame([1, 2, 3, 4, 5, 6]).describe()</lang>

Output:
              0
count  6.000000
mean   3.500000
std    1.870829
min    1.000000
25%    2.250000
50%    3.500000
75%    4.750000
max    6.000000

To get the fivenum values asked for, the pandas.DataFrame.quantile function can be used: <lang python>import pandas as pd pd.DataFrame([1, 2, 3, 4, 5, 6]).quantile([.0, .25, .50, .75, 1.00], interpolation='nearest')</lang>

Output:
      0
0.00  1
0.25  2
0.50  3
0.75  5
1.00  6

The interpolation value supports more of the differing ways of calculation in use.

Python: Functional – without imports

Works with: Python 3 <lang python># fiveNums :: [Float] -> (Float, Float, Float, Float, Float) def fiveNums(xs): 

   def median(xs):
       lng = len(xs)
       m = lng // 2
       return xs[m] if (
           0 != lng % 2
       ) else (xs[m - 1] + xs[m]) / 2

   ys = sorted(xs)
   lng = len(ys)
   m = lng // 2
   return (
       ys[0], 
       median(ys[0:(m + (lng % 2))]),
       median(ys), 
       median(ys[m:]), 
       ys[-1]
   ) if 0 < lng else None
  1. TEST --------------------------------------------------------------------

for xs in [[15, 6, 42, 41, 7, 36, 49, 40, 39, 47, 43], 

          [36, 40, 7, 39, 41, 15],
          [
              0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594,
              0.73438555, -0.03035726, 1.46675970, -0.74621349, -0.72588772,
              0.63905160, 0.61501527, -0.98983780, -1.00447874, -0.62759469,
              0.66206163, 1.04312009, -0.10305385, 0.75775634, 0.32566578
          ]]:
   print(
       fiveNums(xs)
   )</lang>
Output:
(6, 25.5, 40, 42.5, 49)
(7, 15, 37.5, 40, 41)
(-1.95059594, -0.676741205, 0.23324706, 0.746070945, 1.73131507)

R

The fivenum function is built-in, see R manual.

<lang R>x <- c(0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594, 0.73438555,-0.03035726, 1.46675970, -0.74621349, -0.72588772, 0.63905160, 0.61501527, -0.98983780, -1.00447874, -0.62759469, 0.66206163, 1.04312009, -0.10305385, 0.75775634, 0.32566578)

fivenum(x)</lang>

Output 

[1] -1.9505959 -0.6767412  0.2332471  0.7460709  1.7313151

Racket

Racket's =quantile= functions use a different method to Tukey; so a new implementation was made.

<lang racket>#lang racket/base (require math/private/statistics/quickselect)

racket's quantile uses "Method 1" of https://en.wikipedia.org/wiki/Quartile
Tukey (fivenum) uses "Method 2", so we will need a specialist median

(define (fivenum! data-v) 

 (define (tukey-median start end)
   (define-values (n/2 parity) (quotient/remainder (- end start) 2))
   (define mid (+ start n/2))
   (if (zero? parity)
       (/ (+ (data-kth-value! (+ mid (sub1 parity))) (data-kth-value! mid)) 2)
       (data-kth-value! mid)))

 (define n-data (let ((l (vector-length data-v)))
                  (if (zero? l)
                      (raise-argument-error 'data-v "nonempty (Vectorof Real)" data-v)
                      l)))
 
 (define (data-kth-value! n) (kth-value! data-v n <))

 (define subset-size (let-values (((n/2 parity) (quotient/remainder n-data 2))) (+ n/2 parity)))
 
 (vector (data-kth-value! 0)
         (tukey-median 0 subset-size)
         (tukey-median 0 n-data)
         (tukey-median (- n-data subset-size) n-data)
         (data-kth-value! (sub1 n-data))))

(define (fivenum data-seq) 

 (fivenum! (if (and (vector? data-seq) (not (immutable? data-seq)))
               data-seq
               (for/vector ((datum data-seq)) datum))))

(module+ test 

 (require rackunit
          racket/vector)
 (check-equal? #(14 14 14 14 14) (fivenum #(14)) "Minimal case")
 (check-equal? #(8 11 14 17 20) (fivenum #(8 14 20)) "3-value case")
 (check-equal? #(8 11 15 18 20) (fivenum #(8 14 16 20)) "4-value case")

 (define x1-seq #(36 40 7 39 41 15))
 (define x1-v (vector-copy x1-seq))
 (check-equal? x1-seq x1-v "before fivenum! sequence and vector were not `equal?`")
 (check-equal? #(7 15 #e37.5 40 41) (fivenum! x1-v) "Test against Go results x1")
 (check-not-equal? x1-seq x1-v "fivenum! did not mutate mutable input vectors")
 
 (check-equal? #(6 #e25.5 40 #e42.5 49) (fivenum #(15 6 42 41 7 36 49 40 39 47 43)) "Test against Go results x2")
 
 (check-equal? #(-1.95059594 -0.676741205 0.23324706 0.746070945 1.73131507)
               (fivenum (vector 0.14082834  0.09748790  1.73131507  0.87636009 -1.95059594  0.73438555
                                -0.03035726  1.46675970 -0.74621349 -0.72588772  0.63905160  0.61501527
                                -0.98983780 -1.00447874 -0.62759469  0.66206163  1.04312009 -0.10305385
                                0.75775634  0.32566578))
               "Test against Go results x3"))</lang>

This program passes its tests silently.

Raku

(formerly Perl 6)

Translation of: Perl

<lang perl6>sub fourths ( Int $end ) { 

   my $end_22 = $end div 2 / 2;

   return 0, $end_22, $end/2, $end - $end_22, $end;

} sub fivenum ( @nums ) { 

   my @x = @nums.sort(+*)
       or die 'Input must have at least one element';

   my @d = fourths(@x.end);

   return ( @x[@d».floor] Z+ @x[@d».ceiling] ) »/» 2;

}

say .&fivenum for [15, 6, 42, 41, 7, 36, 49, 40, 39, 47, 43], 

                 [36, 40, 7, 39, 41, 15], [
   0.14082834,  0.09748790,  1.73131507,  0.87636009, -1.95059594,
   0.73438555, -0.03035726,  1.46675970, -0.74621349, -0.72588772,
   0.63905160,  0.61501527, -0.98983780, -1.00447874, -0.62759469,
   0.66206163,  1.04312009, -0.10305385,  0.75775634,  0.32566578,

]; </lang>

Output:
(6 25.5 40 42.5 49)
(7 15 37.5 40 41)
(-1.95059594 -0.676741205 0.23324706 0.746070945 1.73131507)

REXX

Programming note:   this REXX program uses a unity─based array. <lang rexx>/*REXX program computes the five─number summary (LO─value, p25, medium, p75, HI─value).*/ parse arg x if x= then x= 15 6 42 41 7 36 49 40 39 47 43 /*Not specified? Then use the defaults*/ say 'input numbers: ' space(x) /*display the original list of numbers.*/ call 5num /*invoke the five─number function. */ say ' five─numbers: ' result /*display " " " results. */ exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ bSort: procedure expose @.; parse arg n; m=n-1 /*N: the number of @ array elements.*/ 

        do m=m  for m  by -1  until ok;   ok= 1 /*keep sorting the  @  array 'til done.*/
          do j=1  for m;   k= j + 1;      if @.j<=@.k  then iterate  /*In order?  Good.*/
          parse value @.j @.k 0  with  @.k @.j ok    /*swap 2 elements;  flag as ¬done.*/
          end   /*j*/
        end     /*m*/;          return

/*──────────────────────────────────────────────────────────────────────────────────────*/ med: arg s,e; $=e-s+1; m=s+$%2; if $//2 then return @.m; _=m-1; return (@._+@.m)/2 /*──────────────────────────────────────────────────────────────────────────────────────*/ 5num: #= words(x); if #==0 then return '***error*** array is empty.' 

      parse var x . 1 LO . 1 HI .               /*assume values for LO and HI (for now)*/
      q2= # % 2;                                er= '***error***  element'
                    do j=1  for #;     @.j= word(x, j)
                    if \datatype(@.j, 'N')  then return  er   j   "isn't numeric: "   @.j
                    LO= min(LO, @.j);  HI= max(HI, @.j)
                    end   /*j*/                /* [↑]  traipse thru array, find min,max*/
      call bSort #                             /*use a bubble sort  (easiest to code). */
      if #//2  then p25= q2                    /*calculate the second quartile number. */
               else p25= q2 - 1                /*    "      "     "       "       "    */
      return LO  med(1, p25)   med(1, #)   med(q2, #)   HI  /*return list of 5 numbers.*/</lang>
output   when using the default input of:     15 6 42 41 7 36 49 40 39 47 43 
input numbers:  15 6 42 41 7 36 49 40 39 47 43
 five─numbers:  6 15 40 42 49
output   when using the (internal) default inputs of:     36 40 7 39 41 15 
input numbers:  36 40 7 39 41 15
 five─numbers:  7 11 37.5 39.5 41

Ruby

Translation of: Perl

<lang ruby>def fivenum(array) 

 sorted_arr = array.sort
 n = array.size
 n4 = (((n + 3).to_f / 2.to_f) / 2.to_f).floor
 d = Array.[](1, n4, ((n.to_f + 1) / 2).to_i, n + 1 - n4, n)
 sum_array = []
 (0..4).each do |e| # each loops have local scope, for loops don't
   index_floor = (d[e] - 1).floor
   index_ceil  = (d[e] - 1).ceil
   sum_array.push(0.5 * (sorted_arr[index_floor] + sorted_arr[index_ceil]))
 end
 sum_array

end

test_array = [15, 6, 42, 41, 7, 36, 49, 40, 39, 47, 43] tukey_array = fivenum(test_array) p tukey_array test_array = [36, 40, 7, 39, 41, 15] tukey_array = fivenum(test_array) p tukey_array test_array = [0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594, 

             0.73438555, -0.03035726, 1.46675970, -0.74621349, -0.72588772,
             0.63905160,  0.61501527, -0.98983780, -1.00447874, -0.62759469,
             0.66206163,  1.04312009, -0.10305385, 0.75775634,  0.32566578]

tukey_array = fivenum(test_array) p tukey_array </lang>

Output:
[6.0, 15.0, 40.0, 43.0, 49.0]
[7.0, 15.0, 36.0, 40.0, 41.0]
[-1.95059594, -0.72588772, 0.14082834, 0.75775634, 1.73131507]

SAS

<lang sas>/* build a dataset */ data test; do i=1 to 10000; x=rannor(12345); output; end; keep x; run;

/* compute the five numbers */ proc means data=test min p25 median p75 max; var x; run;</lang>

Output

Analysis Variable : x
Minimum 25th Pctl Median 75th Pctl Maximum
-4.0692299 -0.6533022 0.0066299 0.6768043 4.1328026

Scala

Array based solution

<lang Scala>import java.util

object Fivenum extends App { 

 val xl = Array(
   Array(15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0),
   Array(36.0, 40.0, 7.0, 39.0, 41.0, 15.0),
   Array(0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594, 0.73438555,
     -0.03035726, 1.46675970, -0.74621349, -0.72588772, 0.63905160, 0.61501527, -0.98983780,
     -1.00447874, -0.62759469, 0.66206163, 1.04312009, -0.10305385, 0.75775634, 0.32566578)
 )

 for (x <- xl) println(f"${util.Arrays.toString(fivenum(x))}%s\n\n")

 def fivenum(x: Array[Double]): Array[Double] = {
   require(x.forall(!_.isNaN), "Unable to deal with arrays containing NaN")

   def median(x: Array[Double], start: Int, endInclusive: Int): Double = {
     val size = endInclusive - start + 1
     require(size > 0, "Array slice cannot be empty")
     val m = start + size / 2
     if (size % 2 == 1) x(m) else (x(m - 1) + x(m)) / 2.0
   }

   val result = new Array[Double](5)
   util.Arrays.sort(x)
   result(0) = x(0)
   result(2) = median(x, 0, x.length - 1)
   result(4) = x(x.length - 1)
   val m = x.length / 2
   val lowerEnd = if (x.length % 2 == 1) m else m - 1
   result(1) = median(x, 0, lowerEnd)
   result(3) = median(x, m, x.length - 1)
   result
 }

}</lang>

Output:

See it running in your browser by ScalaFiddle (JavaScript, non JVM) or by Scastie (JVM).

Sidef

Translation of: Raku

<lang ruby>func fourths(e) { 

   var t = ((e>>1) / 2)
   [0, t, e/2, e - t, e]

}

func fivenum(nums) { 

   var x = nums.sort
   var d = fourths(x.end)

   ([x[d.map{.floor}]] ~Z+ [x[d.map{.ceil}]]) »/» 2

}

var nums = [ 

   [15, 6, 42, 41, 7, 36, 49, 40, 39, 47, 43],
   [36, 40, 7, 39, 41, 15], [
   0.14082834,  0.09748790,  1.73131507,  0.87636009, -1.95059594,
   0.73438555, -0.03035726,  1.46675970, -0.74621349, -0.72588772,
   0.63905160,  0.61501527, -0.98983780, -1.00447874, -0.62759469,
   0.66206163,  1.04312009, -0.10305385,  0.75775634,  0.32566578,

]]

nums.each { say fivenum(_).join(', ') }</lang>

Output:
6, 25.5, 40, 42.5, 49
7, 15, 37.5, 40, 41
-1.95059594, -0.676741205, 0.23324706, 0.746070945, 1.73131507

Stata

First build a dataset:

<lang stata>clear set seed 17760704 qui set obs 10000 gen x=rnormal()</lang>

The summarize command produces all the required statistics, and more:

<lang stata>qui sum x, detail di r(min),r(p25),r(p50),r(p75),r(max)</lang>

Output 

-3.6345866 -.66536 .0026834 .68398139 3.7997103

It's also possible to use the tabstat command

<lang stata>tabstat x, s(mi q ma)</lang>

Output 

    variable |       min       p25       p50       p75       max
-------------+--------------------------------------------------
           x | -3.634587   -.66536  .0026834  .6839814   3.79971
----------------------------------------------------------------

Another example:

<lang stata>clear mat a=0.14082834\0.09748790\1.73131507\0.87636009\-1.95059594\ /// 0.73438555\-0.03035726\1.46675970\-0.74621349\-0.72588772\ /// 0.63905160\0.61501527\-0.98983780\-1.00447874\-0.62759469\ /// 0.66206163\1.04312009\-0.10305385\0.75775634\0.32566578 svmat a tabstat a1, s(mi q ma)</lang>

Output 

    variable |       min       p25       p50       p75       max
-------------+--------------------------------------------------
          a1 | -1.950596 -.6767412  .2332471   .746071  1.731315
----------------------------------------------------------------

VBA

Uses Quicksort.

Translation of: Phix

<lang vb>Option Base 1

Private Function median(tbl As Variant, lo As Integer, hi As Integer) 

   Dim l As Integer: l = hi - lo + 1
   Dim m As Integer: m = lo + WorksheetFunction.Floor_Precise(l / 2)
   If l Mod 2 = 1 Then
       median = tbl(m)
   Else
       median = (tbl(m - 1) + tbl(m)) / 2
   End if

End Function Private Function fivenum(tbl As Variant) As Variant 

   Sort tbl, UBound(tbl)
   Dim l As Integer: l = UBound(tbl)
   Dim m As Integer: m = WorksheetFunction.Floor_Precise(l / 2) + l Mod 2
   Dim r(5) As String
   r(1) = CStr(tbl(1))
   r(2) = CStr(median(tbl, 1, m))
   r(3) = CStr(median(tbl, 1, l))
   r(4) = CStr(median(tbl, m + 1, l))
   r(5) = CStr(tbl(l))
   fivenum = r

End Function Public Sub main() 

   Dim x1 As Variant, x2 As Variant, x3 As Variant
   x1 = [{15, 6, 42, 41, 7, 36, 49, 40, 39, 47, 43}]
   x2 = [{36, 40, 7, 39, 41, 15}]
   x3 = [{0.14082834, 0.09748790, 1.73131507, 0.87636009, -1.95059594, 0.73438555, -0.03035726, 1.46675970, -0.74621349, -0.72588772, 0.63905160, 0.61501527, -0.98983780, -1.00447874, -0.62759469, 0.66206163, 1.04312009, -0.10305385, 0.75775634, 0.32566578}]
   Debug.Print Join(fivenum(x1), " | ")
   Debug.Print Join(fivenum(x2), " | ")
   Debug.Print Join(fivenum(x3), " | ")

End Sub</lang>

Output:
6 | 25,5 | 40 | 43 | 49
7 | 15 | 37,5 | 40 | 41
-1,95059594 | -0,676741205 | 0,23324706 | 0,746070945 | 1,73131507

Visual Basic .NET

Translation of: C#

<lang vbnet>Imports System.Runtime.CompilerServices Imports System.Text

Module Module1 

   <Extension()>
   Function AsString(Of T)(c As ICollection(Of T), Optional format As String = "{0}") As String
       Dim sb As New StringBuilder("[")
       Dim it = c.GetEnumerator()
       If it.MoveNext() Then
           sb.AppendFormat(format, it.Current)
       End If
       While it.MoveNext()
           sb.Append(", ")
           sb.AppendFormat(format, it.Current)
       End While
       Return sb.Append("]").ToString()
   End Function

   Function Median(x As Double(), start As Integer, endInclusive As Integer) As Double
       Dim size = endInclusive - start + 1
       If size <= 0 Then
           Throw New ArgumentException("Array slice cannot be empty")
       End If
       Dim m = start + size \ 2
       Return If(size Mod 2 = 1, x(m), (x(m - 1) + x(m)) / 2.0)
   End Function

   Function Fivenum(x As Double()) As Double()
       For Each d In x
           If Double.IsNaN(d) Then
               Throw New ArgumentException("Unable to deal with arrays containing NaN")
           End If
       Next

       Array.Sort(x)
       Dim result(4) As Double

       result(0) = x.First()
       result(2) = Median(x, 0, x.Length - 1)
       result(4) = x.Last()

       Dim m = x.Length \ 2
       Dim lowerEnd = If(x.Length Mod 2 = 1, m, m - 1)

       result(1) = Median(x, 0, lowerEnd)
       result(3) = Median(x, m, x.Length - 1)

       Return result
   End Function

   Sub Main()
       Dim x1 = {
           New Double() {15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0},
           New Double() {36.0, 40.0, 7.0, 39.0, 41.0, 15.0},
           New Double() {
                    0.14082834, 0.0974879, 1.73131507, 0.87636009, -1.95059594, 0.73438555,
                   -0.03035726, 1.4667597, -0.74621349, -0.72588772, 0.6390516, 0.61501527,
                   -0.9898378, -1.00447874, -0.62759469, 0.66206163, 1.04312009, -0.10305385,
                    0.75775634, 0.32566578
           }
       }
       For Each x In x1
           Dim result = Fivenum(x)
           Console.WriteLine(result.AsString("{0:F8}"))
       Next
   End Sub

End Module</lang>

Output:
[6.00000000, 25.50000000, 40.00000000, 42.50000000, 49.00000000]
[7.00000000, 15.00000000, 37.50000000, 40.00000000, 41.00000000]
[-1.95059594, -0.67674121, 0.23324706, 0.74607095, 1.73131507]

zkl

Uses GNU GSL library. <lang zkl>var [const] GSL=Import("zklGSL"); // libGSL (GNU Scientific Library) fcn fiveNum(v){ // V is a GSL Vector, --> min, 1st qu, median, 3rd qu, max 

  v.sort();
  return(v.min(),v.quantile(0.25),v.median(),v.quantile(0.75),v.max())

}</lang> <lang zkl>fiveNum(GSL.VectorFromData( 

  15.0, 6.0, 42.0, 41.0, 7.0, 36.0, 49.0, 40.0, 39.0, 47.0, 43.0)).println();

println(fiveNum(GSL.VectorFromData(36.0, 40.0, 7.0, 39.0, 41.0, 15.0)));

v:=GSL.VectorFromData( 

  0.14082834,  0.09748790,  1.73131507,  0.87636009, -1.95059594,  0.73438555,
 -0.03035726,  1.46675970, -0.74621349, -0.72588772,  0.63905160,  0.61501527,
 -0.98983780, -1.00447874, -0.62759469,  0.66206163,  1.04312009, -0.10305385,
  0.75775634,  0.32566578);

println(fiveNum(v));</lang>

Output:
L(6,25.5,40,42.5,49)
L(7,20.25,37.5,39.75,41)
L(-1.9506,-0.652168,0.233247,0.740228,1.73132)
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