g01al calculates a five-point summary for a single sample.

Syntax

C#
public static void g01al( int n, double[] x, double[] res, out int ifail )

Visual Basic
Public Shared Sub g01al ( _ n As Integer, _ x As Double(), _ res As Double(), _ <OutAttribute> ByRef ifail As Integer _ )

Visual C++
public: static void g01al( int n, array<double>^ x, array<double>^ res, [OutAttribute] int% ifail )

F#
static member g01al : n : int * x : float[] * res : float[] * ifail : int byref -> unit

Parameters

n: Type: System..::..Int32
On entry: $n$ , number of observations in the sample.

Constraint: $n \geq 5$ .

x: Type: array<System..::..Double>[]()[][]
An array of size [n]
On entry: the sample observations, $x_{1}, x_{2}, \dots, x_{n}$ .

res

Type: array<System..::..Double>[]()[][]

An array of size [

5

]

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.

ifail: Type: System..::..Int32%
On exit: $ifail = 0$ unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

Description

g01al 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

x_{i}

and let

z_{i}

, for

i = 1, 2, \dots, n

, represent the sample observations sorted into ascending order.

Let

m = \frac{n}{2}

n

is even and

\frac{(n + 1)}{2}

n

is odd,

and

k = \frac{m}{2}

m

is even and

\frac{(m + 1)}{2}

m

is odd.

Then we have

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

Error Indicators and Warnings

Errors or warnings detected by the method:

$ifail = 1$

On entry,

n < 5

$ifail = -9000$: An error occured, see message report.
$ifail = -8000$: Negative dimension for array $〈value〉$
$ifail = -6000$: Invalid Parameters $〈value〉$

Accuracy

The computations are stable.

Parallelism and Performance

None.

Further Comments

The time taken by g01al is proportional to

n

Example

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

12