NAG FL Interface
g01alf (five_​point_​summary)

1 Purpose

g01alf calculates a five-point summary for a single sample.

2 Specification

Fortran Interface
Subroutine g01alf ( n, x, iwrk, res, ifail)
Integer, Intent (In) :: n
Integer, Intent (Inout) :: ifail
Integer, Intent (Out) :: iwrk(n)
Real (Kind=nag_wp), Intent (In) :: x(n)
Real (Kind=nag_wp), Intent (Out) :: res(5)
C Header Interface
#include <nag.h>
void  g01alf_ (const Integer *n, const double x[], Integer iwrk[], double res[], Integer *ifail)
The routine may be called by the names g01alf or nagf_stat_five_point_summary.

3 Description

g01alf calculates the minimum, lower hinge, median, upper hinge and the maximum of a sample of n observations.
The data consist of a single sample of n observations denoted by xi and let zi, for i=1,2,,n, represent the sample observations sorted into ascending order.
Let m= n2 if n is even and n+1 2 if n is odd,
and k= m2 if m is even and m+1 2 if m is odd.
Then we have
Minimum =z1,  
Maximum =zn,  
Median =zm if n is odd,
  = zm+zm+12 if n is even, 12
Lower hinge =zk if m is odd,
  = zk+zk+12 if m is even, 12
Upper hinge =zn-k+1 if m is odd,
  = zn-k+zn-k+12 if m is even. 12

4 References

Erickson B H and Nosanchuk T A (1985) Understanding Data Open University Press, Milton Keynes
Tukey J W (1977) Exploratory Data Analysis Addison–Wesley

5 Arguments

1: n Integer Input
On entry: n, number of observations in the sample.
Constraint: n5.
2: xn Real (Kind=nag_wp) array Input
On entry: the sample observations, x1,x2,,xn.
3: iwrkn Integer array Workspace
4: res5 Real (Kind=nag_wp) array Output
On exit: res contains the five-point summary.
The minimum.
The lower hinge.
The median.
The upper hinge.
The maximum.
5: ifail Integer Input/Output
On entry: ifail must be set to 0, -1 or 1. If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value -1 or 1 is recommended. If the output of error messages is undesirable, then the value 1 is recommended. Otherwise, if you are not familiar with this argument, the recommended value is 0. When the value -1 or 1 is used it is essential to test the value of ifail on exit.
On exit: ifail=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry ifail=0 or -1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, n=value.
Constraint: n5.
An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

The computations are stable.

8 Parallelism and Performance

g01alf is not threaded in any implementation.

9 Further Comments

The time taken by g01alf is proportional to n.

10 Example

This example calculates a five-point summary for a sample of 12 observations.

10.1 Program Text

Program Text (g01alfe.f90)

10.2 Program Data

Program Data (g01alfe.d)

10.3 Program Results

Program Results (g01alfe.r)