Question

a. Why is it impossible for a categorical variable to be truly normally distributed? (Answer within the context of mean and standard deviation

Answer 1

Normal distribution is defined by two parameters i.e. mean and standard deviation but in case of categorical variables, finding mean and stardard deviation is practically meaningless. For example, if a categorical variable represents shoe sizes then finding mean shoe size as 6.7 or 5.4 doesn't make sense, only mode will be relevant in this case. So mean doesn't hold any practical meaning in case of categorical variables and hence, it is impossible for a categorical variable to be trully normally distributed.