Expected Value Calculator

The expected value is the single most important summary of a random process, the long-run average you would settle on if you repeated the situation over and over, and this calculator works it out from a list of outcomes and their probabilities. Enter the possible values and the probability of each, and it returns the expected value, the variance and the standard deviation, along with the total of the probabilities so you can check they form a complete distribution, all updating as you type. The idea behind it is intuitive: some outcomes are more likely than others, so a fair average has to weight each value by how often it happens. Multiply every value by its probability, add those products together, and you have the expected value, also called the mean of the distribution. It is the balancing point of the probabilities, and it answers questions like the average roll of a die, the typical payout of a game, or the mean demand a business should plan for. The calculator goes further and reports the spread as well: the variance measures how far outcomes tend to fall from the expected value, and the standard deviation, its square root, expresses that spread in the same units as the values, which tells you how reliable the average is. That makes the tool genuinely useful for statistics and probability students learning distributions and checking homework, for anyone weighing up a bet, an insurance decision or a risky choice, and for business and finance work where outcomes carry probabilities. Because the results recalculate live, you can adjust a probability or add an outcome and immediately see the mean and spread respond. The formulas and a worked example are explained clearly below.

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