# NAG FL Interfaceg01alf (five_​point_​summary)

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## 1Purpose

g01alf calculates a five-point summary for a single sample.

## 2Specification

Fortran Interface
 Subroutine g01alf ( n, x, iwrk, res,
 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)
#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.

## 3Description

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 $m=\frac{n}{2}$ 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.$\phantom{\frac{1}{2}}$

## 4References

Erickson B H and Nosanchuk T A (1985) Understanding Data Open University Press, Milton Keynes
Tukey J W (1977) Exploratory Data Analysis Addison–Wesley

## 5Arguments

1: $\mathbf{n}$Integer Input
On entry: $n$, number of observations in the sample.
Constraint: ${\mathbf{n}}\ge 5$.
2: $\mathbf{x}\left({\mathbf{n}}\right)$Real (Kind=nag_wp) array Input
On entry: the sample observations, ${x}_{1},{x}_{2},\dots ,{x}_{n}$.
3: $\mathbf{iwrk}\left({\mathbf{n}}\right)$Integer array Workspace
4: $\mathbf{res}\left(5\right)$Real (Kind=nag_wp) array Output
On exit: res contains the five-point summary.
${\mathbf{res}}\left(1\right)$
The minimum.
${\mathbf{res}}\left(2\right)$
The lower hinge.
${\mathbf{res}}\left(3\right)$
The median.
${\mathbf{res}}\left(4\right)$
The upper hinge.
${\mathbf{res}}\left(5\right)$
The maximum.
5: $\mathbf{ifail}$Integer Input/Output
On entry: ifail must be set to $0$, $-1$ or $1$ 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 $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.
On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

## 6Error Indicators and Warnings

If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
${\mathbf{ifail}}=1$
On entry, ${\mathbf{n}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{n}}\ge 5$.
${\mathbf{ifail}}=-99$
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
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.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

## 7Accuracy

The computations are stable.

## 8Parallelism and Performance

g01alf is not threaded in any implementation.

The time taken by g01alf is proportional to $n$.

## 10Example

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

### 10.1Program Text

Program Text (g01alfe.f90)

### 10.2Program Data

Program Data (g01alfe.d)

### 10.3Program Results

Program Results (g01alfe.r)