This is a documentation for Siril's statistics, given by the graphical user interface from the contextual menu of images (right-clicking in it) then selecting 'Statistics...', from the Image Information submenu of the application menu after also selecting 'Statistics...' or using the stat command.
Mean: this is the arithmetic mean, also known as average or arithmetic average. This is computed by doing the sum of the values divided by the number of values.
Median: this is the value separating the higher half from the lower half of a data sample. Generally, it represents the value of the background of an astronomical image.
Sigma: this is a measure of the amount of dispersion of the image pixels. The sigma value of a sub image containing only the background will represent the noise of the image.
Background noise: this is a measure of estimated noise in image background level, for pixels having a value low enough to be considered as background. It is an iterative process based on k.sigma, so there is no fixed threshold for the low enough.
Average Deviation: In order to understand what the average deviation is, one needs to understand what the term absolute deviation is. Absolute deviation is the distance between each value in the dataset and that dataset's mean or median. Taking all of these absolute deviations, finding the average, and the mean average deviation is computed.
Median Absolute Deviation (MAD): this is a robust measure of how spread out a set of data is. The absolute deviation and standard deviation are also measures of dispersion, but they are more affected by extremely high or extremely low values.
Bi-Weight Mid-Variance (BWMV): This is yet another tool to measure dispersion of a dataset, even more robust than others cited above to outliers. It discards the data points too far way from the median and computes a weighted variance, weights decreasing as the data points are further way from the median. The estimator of dispersion is the square root of this value.
Location and Scale: In order to align the histograms of the different frames for normalization before stacking, one needs to compute where they are in terms of level and how wide they are in terms of spread. A valid estimator of location could be taken as the median while the MAD or the sqrt(BWMV) (sqrt means square root) could be used for scale. However, in order to give more robustness to the measures, the pixels more than 6 x MAD away from the median are discarded. On this clipped dataset, the median and sqrt(BWMV) are re-computed and used as location and scale estimators respectively.