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:     n IntegerInput
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.
res[0]
The minimum.
res[1]
The lower hinge.
res[2]
The median.
res[3]
The upper hinge.
res[4]
The maximum.
4:     fail NagError *Input/Output
The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6
Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT_ARG_LT
On entry, n=value.
Constraint: n5.
NE_INTERNAL_ERROR
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 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7
Accuracy

The computations are stable.

8
Parallelism and Performance

nag_5pt_summary_stats (g01alc) is not threaded in any implementation.

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)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017