g01 Chapter Contents
g01 Chapter Introduction
NAG Library Manual

# NAG Library Function Documentnag_5pt_summary_stats (g01alc)

## 1  Purpose

nag_5pt_summary_stats (g01alc) calculates a five-point summary for a single sample.

## 2  Specification

 #include #include
 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 $m=\frac{n}{2}$ if $n$ is even and $\frac{\left(n+1\right)}{2}$ if $n$ is odd,
and $k=\frac{m}{2}$ if $m$ is even and $\frac{\left(m+1\right)}{2}$ if $m$ is odd.
Then we have
 Minimum $\text{}={z}_{1}$, Maximum $\text{}={z}_{n}$, Median $\text{}={z}_{m}$ if $n$ is odd, $\text{}=\frac{{z}_{m}+{z}_{m+1}}{2}$ if $n$ is even, $\phantom{\frac{1}{2}}$ Lower hinge $\text{}={z}_{k}$ if $m$ is odd, $\text{}=\frac{{z}_{k}+{z}_{k+1}}{2}$ if $m$ is even, $\phantom{\frac{1}{2}}$ Upper hinge $\text{}={z}_{n-k+1}$ if $m$ is odd, $\text{}=\frac{{z}_{n-k}+{z}_{n-k+1}}{2}$ if $m$ is even.$\phantom{\frac{1}{2}}$
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:    $\mathbf{n}$IntegerInput
On entry: $n$, number of observations in the sample.
Constraint: ${\mathbf{n}}\ge 5$.
2:    $\mathbf{x}\left[{\mathbf{n}}\right]$const doubleInput
On entry: the sample observations, ${x}_{1},{x}_{2},\dots ,{x}_{n}$.
3:    $\mathbf{res}\left[5\right]$doubleOutput
On exit: res contains the five-point summary.
${\mathbf{res}}\left[0\right]$
The minimum.
${\mathbf{res}}\left[1\right]$
The lower hinge.
${\mathbf{res}}\left[2\right]$
The median.
${\mathbf{res}}\left[3\right]$
The upper hinge.
${\mathbf{res}}\left[4\right]$
The maximum.
4:    $\mathbf{fail}$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.
On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.
NE_INT_ARG_LT
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 5$.
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 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.

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 $12$ 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)