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

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khanacademy

Review and intuition why we divide by n-1 for the unbiased sample variance fig 1Review and intuition why we divide by n-1 for the unbiased sample variance fig 2

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