For a statistician, this is insane. In this case, this would mean that a sizable chunk of responders actually receives money from charity.

You seem to assume that every dataset has an inherent mean and standard deviation. But means and standard deviations are the results of modeling a gaussian distribution, and if the model fit is too bad, these metrics simply don't apply for this dataset.

The Lilliefors test was created for exactly this purpose: it gives you the probability that a dataset is not normal distributed. Please use it, or leave out means and standard deviations altogether. The percentiles are (in my - very biased - opinion) much more helpful anyways.

For a statistician, this is insane. In this case, this would mean that a sizable chunk of responders actually

receivesmoney from charity.You seem to assume that every dataset has an inherent mean and standard deviation. But means and standard deviations are the results of modeling a gaussian distribution, and if the model fit is too bad, these metrics simply don't apply for this dataset.

The Lilliefors test was created for exactly this purpose: it gives you the probability that a dataset is not normal distributed. Please use it, or leave out means and standard deviations altogether. The percentiles are (in my - very biased - opinion) much more helpful anyways.