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Loic Guegan 2023-10-18 22:17:39 +02:00
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source/statistics/metrics.rst
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@ -121,9 +121,9 @@ When computing the standard deviation of :math:`X`, we have:
.. math:: .. math::
s^2=\frac{\sum_{i=0}^n (x_i-\overline{x})^2}{n} s^2=\frac{\sum_{i=0}^n (x_i-\overline{x})^2}{n}
In this case, the degree of freedom is :math:`n-1`. As the mean is already known, only :math:`n-1` In this case, the degree of freedom is :math:`n-1`.
of the :math:`x_i` are allowed to vary. In fact, by knowing :math:`n-1` of the :math:`x_i`, we can deduce the last As the mean is already known, only :math:`n-1` of the :math:`x_i` are allowed to vary.
one as follow: Otherwise, the mean changes. In fact, by knowing :math:`n-1` of the :math:`x_i`, we can deduce the last one as follow:
.. math:: .. math::
\overline{x}=\frac{(\sum_{i=1}^{n-1} x_i) + x_n}{n} \Longrightarrow x_n = n\overline{x} - (\sum_{i=1}^{n-1} x_i) \overline{x}=\frac{(\sum_{i=1}^{n-1} x_i) + x_n}{n} \Longrightarrow x_n = n\overline{x} - (\sum_{i=1}^{n-1} x_i)