This expected value calculator allows you to enter potential outcomes and associated probabilities to determine the expected value of a decision.
What is the Expected Value?
The expected value, also known as the mean value, is the total of all potential decision outcomes multiplied by each possibility's probability. Or to put it another way, it is the benefit you would anticipate if you repeatedly made the same choice under the same circumstances.
Formula:
The formula for the expected value in statistics is as follows:
- E (X) = Expected value
- ∑ = sum of outcomes
- µx = Mean
- X = an outcome
- P (X) = probability of an outcome
How to Calculate the Expected Value?
Below is an example for calculating the expected value.
Example
Find the expected value for the following probability distribution using the expected value formula.
X = 1, 2, 3, 4, 5
P (X) = 0.50, 0.20, 0.30, -0.20, -0.10
Solution:
Using the expected value formula:
x | P(x) | xP(x) |
1.00 | 0.50 | 0.50 |
2.00 | 0.20 | 0.40 |
3.00 | 0.30 | 0.90 |
4.00 | -0.20 | -0.80 |
5.00 | -0.10 | -0.50 |
∑x = 15.00 | ∑P(x) = 0.70 | ∑xP(x) = 0.50 |