scipy.stats.iqr#

scipy.stats.iqr(x, axis=None, rng=(25, 75), scale=1.0, nan_policy='propagate', interpolation='linear', keepdims=False)[source]#

Compute the interquartile range of the data along the specified axis.

The interquartile range (IQR) is the difference between the 75th and 25th percentile of the data. It is a measure of the dispersion similar to standard deviation or variance, but is much more robust against outliers [2].

The rng parameter allows this function to compute other percentile ranges than the actual IQR. For example, setting rng=(0, 100) is equivalent to numpy.ptp.

The IQR of an empty array is np.nan.

New in version 0.18.0.

Parameters
xarray_like

Input array or object that can be converted to an array.

axisint or sequence of int, optional

Axis along which the range is computed. The default is to compute the IQR for the entire array.

rngTwo-element sequence containing floats in range of [0,100] optional

Percentiles over which to compute the range. Each must be between 0 and 100, inclusive. The default is the true IQR: (25, 75). The order of the elements is not important.

scalescalar or str, optional

The numerical value of scale will be divided out of the final result. The following string values are recognized:

  • ‘raw’ : No scaling, just return the raw IQR. Deprecated! Use scale=1 instead.

  • ‘normal’ : Scale by \(2 \sqrt{2} erf^{-1}(\frac{1}{2}) \approx 1.349\).

The default is 1.0. The use of scale='raw' is deprecated. Array-like scale is also allowed, as long as it broadcasts correctly to the output such that out / scale is a valid operation. The output dimensions depend on the input array, x, the axis argument, and the keepdims flag.

nan_policy{‘propagate’, ‘raise’, ‘omit’}, optional

Defines how to handle when input contains nan. The following options are available (default is ‘propagate’):

  • ‘propagate’: returns nan

  • ‘raise’: throws an error

  • ‘omit’: performs the calculations ignoring nan values

interpolationstr, optional

Specifies the interpolation method to use when the percentile boundaries lie between two data points i and j. The following options are available (default is ‘linear’):

  • ‘linear’: i + (j - i)*fraction, where fraction is the fractional part of the index surrounded by i and j.

  • ‘lower’: i.

  • ‘higher’: j.

  • ‘nearest’: i or j whichever is nearest.

  • ‘midpoint’: (i + j)/2.

For NumPy >= 1.22.0, the additional options provided by the method keyword of numpy.percentile are also valid.

keepdimsbool, optional

If this is set to True, the reduced axes are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original array x.

Returns
iqrscalar or ndarray

If axis=None, a scalar is returned. If the input contains integers or floats of smaller precision than np.float64, then the output data-type is np.float64. Otherwise, the output data-type is the same as that of the input.

See also

numpy.std, numpy.var

References

1

“Interquartile range” https://en.wikipedia.org/wiki/Interquartile_range

2

“Robust measures of scale” https://en.wikipedia.org/wiki/Robust_measures_of_scale

3

“Quantile” https://en.wikipedia.org/wiki/Quantile

Examples

>>> from scipy.stats import iqr
>>> x = np.array([[10, 7, 4], [3, 2, 1]])
>>> x
array([[10,  7,  4],
       [ 3,  2,  1]])
>>> iqr(x)
4.0
>>> iqr(x, axis=0)
array([ 3.5,  2.5,  1.5])
>>> iqr(x, axis=1)
array([ 3.,  1.])
>>> iqr(x, axis=1, keepdims=True)
array([[ 3.],
       [ 1.]])