# naginterfaces.library.stat.five_​point_​summary¶

naginterfaces.library.stat.five_point_summary(x)[source]

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://www.nag.com/numeric/nl/nagdoc_28.7/flhtml/g01/g01alf.html

Parameters
xfloat, array-like, shape

The sample observations, .

Returns
resfloat, ndarray, shape

contains the five-point summary.

The minimum.

The lower hinge.

The median.

The upper hinge.

The maximum.

Raises
NagValueError
(errno )

On entry, .

Constraint: .

Notes

five_point_summary calculates the minimum, lower hinge, median, upper hinge and the maximum of a sample of observations.

The data consist of a single sample of observations denoted by and let , for , represent the sample observations sorted into ascending order.

Let if is even and if is odd,

and if is even and if is odd.

Then we have

 Minimum =z1, Maximum =zn, Median =zm if n is odd, =zm+zm+12 if n is even, Lower hinge =zk if m is odd, =zk+zk+12 if m is even, Upper hinge =zn−k+1 if m is odd, =zn−k+zn−k+12 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