Expected Value Calculator - Direct Discrete Method
The expected value (also called expectation or mean) represents the average outcome you would expect if you repeated an experiment many times. It is calculated by multiplying each possible outcome by its probability and summing the results.
Enter Outcomes and Probabilities
ValueProbabilityContribution
25.0000
25.0000
-5.0000
Total Probability:1.0000
Expected Value E(X)
45.0000
Variance Var(X)
1825.0000
Standard Deviation σ
42.7200
Probability
E(X) = 45.00
0.25
-20
0.50
50
0.25
100
Outcome Value
Understanding Expected Value
What is Expected Value?
Expected value represents the average outcome you would expect over many trials. It is a weighted average where each outcome is weighted by its probability of occurring.
Interpretation
Positive E(X): On average, you gain value
Negative E(X): On average, you lose value
E(X) = 0: A fair game - neither gain nor loss on average
Common Applications
Games: Determining if a game is favorable
Investments: Comparing expected returns
Insurance: Calculating fair premiums
Decision Making: Choosing between uncertain options
Variance and Standard Deviation
While expected value tells you the average outcome, variance and standard deviation measure how spread out the outcomes are:
Low variance: Outcomes are clustered near the expected value
High variance: Outcomes are more spread out (higher risk)
Standard deviation (σ): Square root of variance, in same units as outcomes