The hare and the tortoise had to take a make-up class in Maths over summer, a two-month, self-paced course with a test at the end of each of 12 chapters. The course requires a 70% grade to pass.
In the first month, they both had difficulties with the concepts. The hare averaged 60% on his exams; the tortoise averaged 50%. The owl, the supervisor, spent three days of the next week helping them with their difficulties.
It worked. In the second month, the hare averaged 90% on his exams; the tortoise averaged 80%.
However, the tortoise got a passing grade of 75% in the class; the hare failed with 65%. When the hare protested to owl that he’d outscored the tortoise in both months, the owl made the Hare do the Maths on the board—and sign up for another make-up class, after school in autumn.
How did the tortoise pass while the hare flunked?
Answer
In the first month, the hare took 10 chapter tests; the tortoise took only 2. In the second month, the hare took his remaining 2 exams and the tortoise took the 10 he needed to finish.
Hare’s average = (1060 + 290) / 12 = 780/12 = 65
Tortoise’s average = (250 + 1080)/12 = 900/12 = 75
Mathematicians know this as Simpson’s paradox.
