mean


 * __Mean__**

The mean (or expected value) is defined (by Baye in the textbook) as the sum of all probabilities multiplied by the payoffs that occur. Baker’s example of the game show contestant who has won $10,000 and has been given the choice of leaving with the money or playing for more money is a good example. In this case, the contestant knows that there is a 50% chance of winning an additional $12,000 (making the total winnings $22,000) if he chooses to play again. Therefore, the expected value of playing again is $1,000. This is calculated by subtracting the expected value of quitting ($10,000) from the expected value of playing again, which is $11,000 (0.5 times $22,000).


 * __References__**

Baye, Micheal R. __Managerial Economics and Business Strategy__. 2006, pp. 435-436 Samuel A. Baker, copyright 1999-2001 http://hspm.sph.sc.edu/COURSES/ECON/RiskA/RiskA.html


 * __Sample Test Questions__**

A person is planting bulbs in a flower bed in the fall. There is an equal number of bulbs that will produce red flowers, yellow flowers, or blue flowers. Let's say that red flowers are worth $3, yellow flowers are worth $2, and blue flowers are worth $1. If only one bulb grows and blooms in the fall, what is the expected value of the flower?

a. $1.00 b. $5.00 c. $3.00 d. $1.98

The answer is d. The mean (or expected value) is calculated by determining the likelihood of each color of flower and multiplying that percentage by the value of each color of flower:

Ex = 1/3 ($3) + 1/3 ($2) + 1/3 ($1) Ex = .33 ($3) + .33 ($2) + 1/3 ($1) Ex = 0.99 + 0.66 + 0.33 $1.98

An economics student has up to 5 chances to take a quiz, but each time the student takes the quiz, the score earned on the previous quiz is erased. The student is trying to decide whether to take the quiz for the fifth time or whether it would be best to be satisfied with the fourth score. What is the student's expected value for the fifth quiz if the scores from the first four attempts are 6, 10, 7, and 12 respectively, out of a possible 14?

a. 8.75 b. 5 c. 11 d. 6

The correct answer is a, 8.75. The expected value (or mean) is calculated by adding up the probabilties that each outcome will occur and multiplying these by the payoffs for each individual outcome.

Ex = ¼(6) + ¼(10) + ¼(7) + ¼(12) = 0.25(6) + 0.25(10) + 0.25(7) + 0.25(12) = 1.5 + 2.5 + 1.75 + 3 = 8.75