Expected Value Calculator - Direct Data

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

-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

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

Understanding Expected Value

Formula and Calculation

Applications

Calculate Expected Value

Use the calculator below to compute the expected value with step-by-step solutions and detailed explanations.