NAG Library Function Document

nag_5pt_summary_stats (g01alc)

▸▿ 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

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

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: $n$ – IntegerInput

On entry:

n

, number of observations in the sample.

Constraint:

n \geq 5

2: $x [n]$ – const doubleInput

On entry: the sample observations,

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

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 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.2.1.2 in the Essential Introduction 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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 3.6.6 in the Essential Introduction for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 3.6.5 in the Essential Introduction for further information.

7 Accuracy

The computations are stable.

8 Parallelism and Performance

Not applicable.

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