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, settingrng=(0, 100)
is equivalent tonumpy.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.
 rngTwoelement 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. Arraylike 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
 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. 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.
 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 thannp.float64
, then the output datatype isnp.float64
. Otherwise, the output datatype is the same as that of the input.
Notes
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 tonumpy.percentile
andnumpy.nanpercentile
that affect the operation of this function. The following modifications apply: Below 1.10.0nan_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 nondefault values. However, multiple axes are still supported.
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.]])