13 Review and intuition why we divide by n-1 for the unbiased sample variance#

%%html
<iframe width="700" height="400" src="https://www.youtube.com/embed/KkaU2ur3Ymw/" frameborder="0" allowfullscreen></iframe>

Review and intuition why we divide by n-1 for the unbiased sample variance fig 1

	population (parameter)	sample (statistic)
mean	$$ \mu = \frac{ \sum_{i=1}^{N} x_{i} }{N} $$	$$ \bar{x} = \frac{ \sum_{i=1}^{n} x_{i} }{n} $$
variance	$$ \sigma^{2} = \frac{ \sum_{i=1}^{N} (x_{i} - \mu)^{2} }{N} $$	$$ S^{2} = \frac{ \sum_{i=1}^{n} (x_{i} - \bar{x})^{2} }{n} $$ S_{n-1}^{2} = \frac{ \sum_{i=1}^{n} (x_{i} - \bar{x})^{2} }{n} $$

# plot data on number line

	population (parameter)	sample (statistic)
mean	$\( \mu = \frac{ \sum_{i=1}^{N} x_{i} }{N} \)$	$\( \bar{x} = \frac{ \sum_{i=1}^{n} x_{i} }{n} \)$
variance	$\( \sigma^{2} = \frac{ \sum_{i=1}^{N} (x_{i} - \mu)^{2} }{N} \)$	$\( S^{2} = \frac{ \sum_{i=1}^{n} (x_{i} - \bar{x})^{2} }{n} \)\( \)\( S_{n-1}^{2} = \frac{ \sum_{i=1}^{n} (x_{i} - \bar{x})^{2} }{n} \)$

Statstics with Python