# 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 None, default: None

If an int, the axis of the input along which to compute the statistic. The statistic of each axis-slice (e.g. row) of the input will appear in a corresponding element of the output. If None, the input will be raveled before computing the statistic.

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 infavor of scale=1 and will raise an error in SciPy 1.12.0. 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’, ‘omit’, ‘raise’}

Defines how to handle input NaNs.

• propagate: if a NaN is present in the axis slice (e.g. row) along which the statistic is computed, the corresponding entry of the output will be NaN.

• omit: NaNs will be omitted when performing the calculation. If insufficient data remains in the axis slice along which the statistic is computed, the corresponding entry of the output will be NaN.

• raise: if a NaN is present, a ValueError will be raised.

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, default: False

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

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.

Notes

Beginning in SciPy 1.9, np.matrix inputs (not recommended for new code) are converted to np.ndarray before the calculation is performed. In this case, the output will be a scalar or np.ndarray of appropriate shape rather than a 2D np.matrix. Similarly, while masked elements of masked arrays are ignored, the output will be a scalar or np.ndarray rather than a masked array with mask=False.

References

Examples

>>> import numpy as np
>>> 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.]])