Introduction to Statistics

Question

Suppose that 200 employees at a major theme park are surveyed, and 54% are under the age of 25.

a. True or False: Of those surveyed, the mean age must be under 25.

b. True or False: Of those surveyed, the median age must be under 25.

Answer 1

Let's start this question by suggesting a possible scenario which fits the facts we are given. 54% of 200 employees are younger than 25. It is possible that all 108 of these employees are 24 years old. (54% of 200 = (54 / 100) *200 = 108.) There are 92 other employees, who could all be 64 (ready to retire when the hit 65!)

If this were true, the mean would be (108 * 24 + 92 * 64) / 200 = (2,592 + 5,888) / 200 = 6,480 / 200 = 32.4.

So it is quite possible that the mean age of the employees would be over 25.

However, when we line up all 200 employees from youngest to oldest and pick the middle one, we will be picking the gap between the 100th person and the 101st person. Since the first 108 employees are all under 25, the 100th and 101st people will definitely be under 25, so the median must be under 25.