nag_5pt_summary_stats (g01alc) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG Library Manual

NAG Library Function Document

nag_5pt_summary_stats (g01alc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_5pt_summary_stats (g01alc) calculates a five-point summary for a single sample.

2  Specification

#include <nag.h>
#include <nagg01.h>
void  nag_5pt_summary_stats (Integer n, const double x[], double res[], NagError *fail)

3  Description

nag_5pt_summary_stats (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:     nIntegerInput
On entry: n, number of observations in the sample.
Constraint: n5.
2:     x[n]const doubleInput
On entry: the sample observations, x1,x2,,xn.
3:     res[5]doubleOutput
On exit: res contains the five-point summary.
The minimum.
The lower hinge.
The median.
The upper hinge.
The maximum.
4:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

Dynamic memory allocation failed.
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.

7  Accuracy

The computations are stable.

8  Parallelism and Performance

Not applicable.

9  Further Comments

The time taken by nag_5pt_summary_stats (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)

nag_5pt_summary_stats (g01alc) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2014