Minimum	$= z_{1}$ ,
Maximum	$= z_{n}$ ,
Median	$= z_{m}$	if $n$ is odd,
	$= \frac{z_{m} + z_{m + 1}}{2}$	if $n$ is even,
Lower hinge	$= z_{k}$	if $m$ is odd,
	$= \frac{z_{k} + z_{k + 1}}{2}$	if $m$ is even,
Upper hinge	$= z_{n - k + 1}$	if $m$ is odd,
	$= \frac{z_{n - k} + z_{n - k + 1}}{2}$	if $m$ is even.

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

Parameters

Compulsory Input Parameters

1: $x (n)$ – double array: The sample observations, $x_{1}, x_{2}, \dots, x_{n}$ .

Optional Input Parameters

1: $n$ – int64int32nag_int scalar: Default: the dimension of the array x.
$n$ , number of observations in the sample.

Constraint: $n \geq 5$ .

Output Parameters

1: $res (5)$ – double array

res contains the five-point summary.

$res (1)$: The minimum.
$res (2)$: The lower hinge.
$res (3)$: The median.
$res (4)$: The upper hinge.
$res (5)$: The maximum.

2: $ifail$ – int64int32nag_int scalar

ifail = 0

unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$

On entry,

n < 5

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

The computations are stable.

Further Comments

The time taken by nag_stat_5pt_summary (g01al) is proportional to

n

Example

This example calculates a five-point summary for a sample of

12

observations.

Open in the MATLAB editor: g01al_example

function g01al_example


fprintf('g01al example results\n\n');

x = [12     9     2     5     6     8 ...
      2     7     3     1    11    10];

[res, ifail] = g01al(x);

fprintf('Maximum                    %14.4f\n', res(5));
fprintf('Upper Hinge (75%% quantile) %14.4f\n', res(4));
fprintf('Median      (50%% quantile) %14.4f\n', res(3));
fprintf('Lower Hinge (25%% quantile) %14.4f\n', res(2));
fprintf('Minimum                    %14.4f\n', res(1));

g01al example results

Maximum                           12.0000
Upper Hinge (75% quantile)         9.5000
Median      (50% quantile)         6.5000
Lower Hinge (25% quantile)         2.5000
Minimum                            1.0000

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox