Suppose a school has three classes, A, B and C, holding 20, 60 and 100 students. What is the average number of students in a class? Well, it depends on who you ask. Let’s understand this deeper.
If you ask the school principal, she will give you 60 as the average number. It’s simple, (20 + 60 + 100) / 3 = 60. But what happens if you choose to sample 50 students and ask them about the number of students in their classes and then average it?
You wait at the school bus stop and randomly select 50 students. Since the sampling is random, you are likely to catch the following numbers from each class.
The probability of finding a student from class A = (20/180). Therefore, the number of students from class A in the total sample of 50 = 50 x (20/180) = 5.55, about 6.
Similarly, from class B, you catch 50 x (60 / 180) = 16.66 or about 17 students, and from class C, 50 x (100 / 180) = 27.77 or about 28 students.
So what are the responses from the students? 5.55 will say 20 students in their class because they are from class A. 16.66 will say 60, and 27.77 says 100. So, the survey average is (5.55 x 20 + 16.66 x 60 + 27.77 x 100) / (5.55 + 16.66 + 27.77) = 3887.6 / 50 = 77.8.
So from the school, you get 60, and from the survey, 78, and no one is lying.
