NAG Library Manual, Mark 27

Interfaces: FL CL AD

NAG CL Interface Introduction

G01 (Stat) Chapter Contents

G01 (Stat) Chapter Introduction

g01al: FL CL AD

NAG CL Interface
g01alc (five_point_summary)

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NAG Library Manual, Mark 27

Interfaces: FL CL AD

NAG CL Interface Introduction

G01 (Stat) Chapter Contents

G01 (Stat) Chapter Introduction

g01al: FL CL AD

▸▿ Contents

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

8 Parallelism and Performance

9 Further Comments

▸▿ 10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

© The Numerical Algorithms Group Ltd. 2019

1 Purpose

g01alc calculates a five-point summary for a single sample.

2 Specification

#include <nag.h>

void	g01alc (Integer n, const double x[], double res[], NagError *fail)

The function may be called by the names: g01alc, nag_stat_five_point_summary or nag_5pt_summary_stats.

3 Description

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

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}

if

n

is even and

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

if

n

is odd,

and

k = \frac{m}{2}

if

m

is even and

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

if

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: $x [n]$ – const double Input

On entry: the sample observations,

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

.

3: $res [5]$ – double Output

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 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_INT_ARG_LT: On entry, $n = 〈value〉$ .
Constraint: $n \geq 5$ .
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 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.

7 Accuracy

The computations are stable.

8 Parallelism and Performance

g01alc is not threaded in any implementation.

9 Further Comments

The time taken by 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 Library Manual, Mark 27

Interfaces: FL CL AD

NAG CL Interface Introduction

G01 (Stat) Chapter Contents

G01 (Stat) Chapter Introduction

g01al: FL CL AD

© The Numerical Algorithms Group Ltd. 2019