I have a database with more than 50000 observations. I have applied non-parametric tests to determine the normality of the data but in any case p<0.05, rejecting the null hypothesis of normality (in many cases, graphically, the histograms appear to follow a bimodal distribution). However, to elaborate a table, I don't know if it would be better to determine mean and standard deviation or median and median absolute deviation, since following the Central Limit Theorem (CLT), when the sample is large enough, it can approximate a normal distribution.

Furthermore, for the determination of normality by means of statistical contrasts, since the Shapiro-Wilk test cannot be used due to the large number of observations, would it be better to use the Kolmogorov-Smirnov test or the Anderson-Darling test?

Thanks,

David