1. Relationships Among Total, Average, and Marginal Data

2. Copyright© 2006 Southwestern/Thomson Learning All rights reserved. Relationships Among Total, Average, and Marginal Data ●Or, to put equivalently, ●Total = average  the number of units ●Or, to put equivalently, ●Total = average  the number of units

3. Copyright© 2006 Southwestern/Thomson Learning All rights reserved. Relationships Among Total, Average, and Marginal Data ●Marginal value of the X-th unit = total value of x units - total value of (X − 1) units. ●Total value of X units = sum of marginal values of the first X units. ●Marginal value of the X-th unit = total value of x units - total value of (X − 1) units. ●Total value of X units = sum of marginal values of the first X units.

4. TABLE 1: Weights of Persons in a Room (in pounds) Copyright © 2006 South-Western/Thomson Learning. All rights reserved.

5. Copyright© 2006 Southwestern/Thomson Learning All rights reserved. ●The marginal, average and total values for the first unit are usually equal. ♦If marginal < average, the average is falling. ♦If marginal > average, the average is rising. ♦If marginal = average, the average is constant; that is, the average is at a maximum or minimum. ●The marginal, average and total values for the first unit are usually equal. ♦If marginal < average, the average is falling. ♦If marginal > average, the average is rising. ♦If marginal = average, the average is constant; that is, the average is at a maximum or minimum. Relationships Among Total, Average and Marginal Data

6. FIGURE 1: Relationship Between Marginal and Average Curves Copyright © 2006 South-Western/Thomson Learning. All rights reserved. F E A D B C Average weight Marginal weight Marginal and Average Weight (pounds) Number of Persons 6543210 50 100 150