scipy.stats.iqr(x, axis=None, rng=(25, 75), scale='raw', 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 [R592].

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.


x : array_like

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

axis : int or sequence of int, optional

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

rng : Two-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.

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

The default is ‘raw’. 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. ‘propagate’ returns nan, ‘raise’ throws an error, ‘omit’ performs the calculations ignoring nan values. Default is ‘propagate’.

interpolation : {‘linear’, ‘lower’, ‘higher’, ‘midpoint’, ‘nearest’}, optional

Specifies the interpolation method to use when the percentile boundaries lie between two data points i and j:

  • ‘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.

Default is ‘linear’.

keepdims : bool, 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.


iqr : scalar 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


This function is heavily dependent on the version of numpy that is installed. Versions greater than 1.11.0b3 are highly recommended, as they include a number of enhancements and fixes to numpy.percentile and numpy.nanpercentile that affect the operation of this function. The following modifications apply:

Below 1.10.0 : nan_policy is poorly defined.
The default behavior of numpy.percentile is used for ‘propagate’. This is a hybrid of ‘omit’ and ‘propagate’ that mostly yields a skewed version of ‘omit’ since NaNs are sorted to the end of the data. A warning is raised if there are NaNs in the data.
Below 1.9.0: numpy.nanpercentile does not exist.
This means that numpy.percentile is used regardless of nan_policy and a warning is issued. See previous item for a description of the behavior.
Below 1.9.0: keepdims and interpolation are not supported.
The keywords get ignored with a warning if supplied with non-default values. However, multiple axes are still supported.


[R591]“Interquartile range”
[R592](1, 2) “Robust measures of scale”


>>> from scipy.stats import iqr
>>> x = np.array([[10, 7, 4], [3, 2, 1]])
>>> x
array([[10,  7,  4],
       [ 3,  2,  1]])
>>> iqr(x)
>>> 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.]])

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