The members of each basketball team wear numbers on their jerseys. What scale of measurement are these numbers considered?  Nominal Ordinal Interval Ratio

Answer:

Nominal scale
Only the most simple operations, such as equivalence and set membership, are possible between the data collected at this scale of measurement. Examples include both dichotomous nominal data, such as 'male' vs. 'female' when measuring gender, 'sedimentary' vs. 'non-sedimentary' when measuring rocks, etc, and non-dichotomous consisting of multiple values, such as 'British', 'American', 'Australian' etc when measuring nationality. Higher operations which imply order, such as 'greater-than' or 'lower-than', are not possible for such data. Neither the mean nor the median can be calculated, the central tendency can be given only by the mode.
This is the reason why the data collected at the nominal scale are sometimes called qualitative data and are sometimes treated as having nothing in common with the quantitative data. Nonetheless, even at this level regression analysis is possible, using dummy variables; for example, gender can be treated as a dummy variable equaling 0 for subjects of male gender and 1 for subjects of female gender. They can be used either as an independent variable (explanatory variable) in an ordinary least squares regression, or as dependent variables in the probit or logistic regression.
Categorical variables
If dichotomous data happen to be randomly distributed, they are called binary, which is characterized by Bernoulli distribution. The Binomial distribution is useful for data comprised of successes and failures.
If non-dichotomous data happen to be randomly distributed, they are called multi-way (or K-way for some specific value of K), which is characterized by a categorical distribution. Both are called categorical variables.