naginterfaces.library.stat.five_​point_​summary

naginterfaces.library.stat.five_point_summary(x)

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

For full information please refer to the NAG Library document for g01al

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/g01/g01alf.html

Parameters

xfloat, array-like, shape $\left(n\right)$

The sample observations, $x_1,x_2,\dots ,x_n$.

Returns

resfloat, ndarray, shape $\left(5\right)$

$res$ contains the five-point summary.

$res\left[0\right]$

The minimum.

$res\left[1\right]$

The lower hinge.

$res\left[2\right]$

The median.

$res\left[3\right]$

The upper hinge.

$res\left[4\right]$

The maximum.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 5$.

Notes

five_point_summary 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.

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