NAG CL Interface
g01alc (five_​point_​summary)

1 Purpose

g01alc calculates a five-point summary for a single sample.

2 Specification

#include <nag.h>
void  g01alc (Integer n, const double x[], double res[], NagError *fail)
The function may be called by the names: g01alc, nag_stat_five_point_summary or nag_5pt_summary_stats.

3 Description

g01alc 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: x[n] const double Input
On entry: the sample observations, x1,x2,,xn.
3: res[5] double Output
On exit: res contains the five-point summary.
The minimum.
The lower hinge.
The median.
The upper hinge.
The maximum.
4: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument value had an illegal value.
On entry, n=value.
Constraint: n5.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL 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 CL Interface for further information.

7 Accuracy

The computations are stable.

8 Parallelism and Performance

g01alc is not threaded in any implementation.

9 Further Comments

The time taken by g01alc 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 (g01alce.c)

10.2 Program Data

Program Data (g01alce.d)

10.3 Program Results

Program Results (g01alce.r)