Standard deviation of the meanΒΆ
The mean value can be calculated by:
$$ \bar x = \frac{1}{N}\sum_{i = 1}^{N}x_i $$
Standard deviation of the individual measurement from the mean
$$ \sigma_x = \sqrt{\frac{1}{N - 1}\sum_{i = 1}^{N}(x_i - \bar x_i)^2} $$ Standard deviation of the mean
$$ \sigma_{\bar x} = \sqrt{\frac{1}{N(N - 1)}\sum_{i = 1}^{N}(x_i - \bar x_i)^2} $$