ABSTRACT
As a part of a program in mathematics a class of 50 children was given a quiz consisting of five questions. Let X be the number of questions answered correctly by each student. Clearly X can assume the values 0, 1, 2, 3, 4 or 5. How would you determine the average score in the class? When we consider the entire class, there are 50 values which X takes on. Some are obviously repetitions since X takes on only six distinct values. The quiz results might be summarized as:
Number correct 0 1 2 3 4 5
Number of students 2 2 6 20 15 5
We could obtain the average by adding the 50 individual scores and then dividing by 50. Due to the repetitions in the observations, the average can be obtained as a weighted average:
the observations might be summarized as:
Number correct 0 1 2 3 4 5
Number of students n0 nx n2 n3 n4 n5
5 where E._q n^ = N, the total number of students. Based on the concept of approximating probabilities by relative frequencies, we would say that the quantities n0/N , n j/N , . . . , n5/N would approach the probability of a child having 0, 1, . . . , 5 correct answers, respectively, as N increases.
