Question

There is a popular phrase "comparing apples to oranges" that reflects problems of comparison. Explain what people mean by "you shouldn't compare apples to oranges" and how the z-distribution could solve that
problem. Give your own personal examples.

Answer 1

We can’t compare two different things which have different distribution. If two items or variables from different categories we need to compare, then we cannot compare these two items directly; but we can compare it relatively. The z-score plays an important role in comparing two different things relatively. It is not direct comparison. Actually, z-score is the score of comparison regarding the mean and standard deviation of the family or sample of the variable. Suppose, you want to compare two students having two different major subjects, then we can compare these two students by finding their z-scores. We cannot compare these two students directly. We need to see background distribution of the scores. So, we cannot simply say that the Math student with 55 marks have less marks than the history student having 64 marks. Instead of this direct comparison, we use z-scores for this comparison. In this way, people expected that we could not compare apples to oranges directly, but we can compare apples and oranges relatively. The comparison by using z-score is not direct comparison but it is a relative comparison. It items or variables for comparison from two different categories, then we need to use z-scores for their relative comparison.