Why in statistics is the average used instead of the median, why are P values for example always calculated with averages and not with median?
I have always been taught that stats and P values always have to be used with the average and I have no idea why, is it just a systemic choice of the person who created the data or can they be used interchangeably for the majority of statistical work?
The $p$-values that are calculated typically rely on the assumption that the data studied are well represented by a specific model. This is often assumed to be the normal distribution that is parameterised by its mean and standard deviation.
The mathematical derivations to produce $p$-values are much more straightforward when making this kind of model assumption (i.e. one that relies use of the mean).
The median is an example of an order statistic. It definitely has nice properties as a summary measure for a data set (e.g. not too sensitive to outliers) but it is harder to use it in a model that can in turn be used to produce $p$-values.