Question

Why do descriptive statistics differ for variables with different levels of measurement?

Answer 1

For different level of measurements of the variables (nominal, ordinal, interval, ratio), there is a different level of detail provided by each of them. Nominal level provides the least amount of detail, ordinal level provides more detail than nominal and interval & ratio scale provides the most.
In the nominal level of measurement, variables are categorical and have no order. Therefore, the descriptive statistics used are frequencies & percentages.
In the ordinal scale, variables are categorical but they have a meaningful order. These are also described using frequencies and %ages.
In the interval/ratio scale, it is a continuous level of measurement. The descriptive statistics used are the mean, median, mode, standard deviation etc.