# scipy.stats.iqr

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

  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
    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. 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

    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.

    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.

  Returns
    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`

  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 to `numpy.percentile` and `numpy.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 non-default 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.]])

scipy.stats.gstd scipy.stats.sem