.. _book_fig_chapter3_fig_cauchy_median_mean:


Median and Mean for Cauchy distribution
---------------------------------------
Figure 3.12.

The bottom panel shows a sample of N points drawn from a Cauchy distribution
with :math:`\mu = 0` and :math:`\gamma=2`. The top panel shows the sample
median, sample mean, and two robust estimates of the location parameter
(see text) as a function of the sample size (only points to the left from
a given sample size are used). Note that the sample mean is not a good
estimator of the distribution's location parameter. Though the mean appears
to converge as N increases, this is deceiving: because of the large tails
in the Cauchy distribution, there is always a high likelihood of a far-flung
point affecting the sample mean. This behavior is markedly different from a
Gaussian distribution where the probability of such "outliers" is much smaller.



.. image:: ../images/chapter3/fig_cauchy_median_mean_1.png
    :scale: 100
    :align: center


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