Estimating Sample Skewness from Sample Data Summaries and Associated Evaluation of Normality

We propose a method to estimate a sample skewness from the given summary statistics and give explicit formulas for the most common scenarios. We show that our method provides a nearly unbiased estimator for the non-parametric skewness measure. We empirically evaluate the performance on real-life data sets of COVID-19 vaccination status. We also demonstrate how the method can be applied to detect the skewness of the underlying distribution.