High School Expected Value Calculator
Calculate the long-run average value of a discrete random variable.
Data Table
| Outcome (x) | Prob P(x) | Action |
|---|
Results
Expected Value E[X]
Variance (σ²)
Std Dev (σ)
Probability Distribution
Using the Expected Value Calculator
The concept of Expected Value (often denoted as E[X] or μ) is central to probability theory and statistics. Fundamentally, it represents the average outcome of a random variable over a large number of experiments. Furthermore, you can think of it as a “weighted average” where each possible outcome is weighted by its probability of occurring.
The Formula
For a discrete random variable X with possible outcomes x₁, x₂, …, xₙ and corresponding probabilities P(x₁), P(x₂), …, P(xₙ):
In practice, this means you multiply each outcome by its probability and subsequently sum all the products together.
Why use an Expected Value Calculator?
Calculating weighted averages manually is tedious, especially when checking if probabilities sum to 1 or when calculating Variance. Fortunately, this tool handles the arithmetic instantly. More importantly, it visualizes the Expected Value as the “Center of Mass.” For instance, if you placed weights on a seesaw corresponding to the probabilities at their respective x-locations, the Expected Value is exactly where the fulcrum must be placed to balance the seesaw.
FAQ
Yes, this tool is completely free for students, teachers, and anyone studying statistics.
Probabilities must sum to 1 (100%) to be valid. If they don’t, this calculator will automatically “normalize” them relative to their total sum so you can still see the distribution shape.
No. Expected Value predicts the average over the long run. In a single event, you will get one of the specific outcomes, not necessarily the Expected Value itself.
Variance measures how spread out the data is from the Expected Value. A high variance means outcomes are widely scattered; low variance means they are clustered near the average.