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