g01 Chapter Contents
g01 Chapter Introduction
NAG C 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.$\phantom{\frac{1}{2}}$

## 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:     nIntegerInput
On entry: $n$, number of observations in the sample.
Constraint: ${\mathbf{n}}\ge 5$.
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.
${\mathbf{res}}\left[0\right]$
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:     failNagError *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.
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.

## 7  Accuracy

The computations are stable.

## 8  Further Comments

The time taken by nag_5pt_summary_stats (g01alc) is proportional to $n$.

## 9  Example

This example calculates a five-point summary for a sample of $12$ observations.

### 9.1  Program Text

Program Text (g01alce.c)

### 9.2  Program Data

Program Data (g01alce.d)

### 9.3  Program Results

Program Results (g01alce.r)