A teacher keeps track of the number of absences in a class each day along with their probabilities.

Question

A teacher keeps track of the number of absences in a class each day along with their probabilities. Her results are in this table.

Number of Absences	Probability
0	0.10
1	0.15
2	0.30
3	0.25
4	0.20

What is the expected number of absences for any given day?

A. 1.8

B. 3.2    

C. 3.8

D. 2.3

Answer 1

An expected value is the same as a mean, which is an average. In this case, it is a weighted average, and the probabilities of the outcomes are their "weights." One straightforward way is to multiply each outcome by its respective probability of occurrence, and add those products together:

(0)(0.10) + (1)(0.15) + (2)(0.30) + (3)(0.25) + (4)(0.20) = 2.3.

Graphing calculators can do this also if you put the number of absences in list 1, and the probability of each in list 2. Then if you calculate the 1-variable stats with list 2 being the frequency list, the calculator will give you lots of statistical values. Topping the list will be x-bar, which is the mean, or the expected value of 2.3.