What does the Mean Mean?

Thought Questions:

• Suppose the average age (mean) for students in the class is 21 years. What do we know about the distribution of students' ages for this class (e.g., Are they all about 21 years old?)? Explain.

• Where does that number (21) come from? Explain.

Deviations:

The deviation is the distance of a data point from the mean of the group. It can be calculated by taking the data point and subtracting the mean (). The sum of the deviations on the left (negative) has the equal the sum of the deviations on the right (positive).

Part 1

Each of the following scenarios is based on 10 students and their ages. The goal of the exercise is to keep the mean at 21.

1. For the following graph:

Nine student ages are represented below. Calculate the deviations on each side, and then sum them together. Use this information to help you decide where to place the 10^th dot to keep the mean at 21.

Sum of Left Deviations	Sum of Right Deviations	Sum of Total Deviations

2117 18 19 20 21 22 23 2419 20 21 22 23 24