Integer, Intent (In)	::	n
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	iwrk(n)
Real (Kind=nag_wp), Intent (In)	::	x(n)
Real (Kind=nag_wp), Intent (Out)	::	res(5)

C Header Interface

#include <nag.h>

void	g01alf_ (const Integer n, const double x[], Integer iwrk[], double res[], Integer ifail)

The routine may be called by the names g01alf or nagf_stat_five_point_summary.

3 Description

g01alf 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.

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:

n \geq 5

2: $x (n)$ – Real (Kind=nag_wp) array Input

On entry: the sample observations,

x_{1}, x_{2}, \dots, x_{n}

3: $iwrk (n)$ – Integer array Workspace

4: $res (5)$ – Real (Kind=nag_wp) array Output

On exit: 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.

5: $ifail$ – Integer Input/Output

On entry: ifail must be set to

0

−1

1

to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of

0

causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of

−1

means that an error message is printed while a value of

1

means that it is not.

If halting is not appropriate, the value

−1

1

is recommended. If message printing is undesirable, then the value

1

is recommended. Otherwise, the value

0

is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit:

ifail = 0

unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 5$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

The computations are stable.

8 Parallelism and Performance

g01alf is not threaded in any implementation.

9 Further Comments

The time taken by g01alf is proportional to

n

10 Example

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

12

observations.

g01al: FL CL CPP AD

NAG FL Interfaceg01alf (five_​point_​summary)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
g01alf (five_point_summary)