Discrete Variance Calculator | Calculate Var[X] Easily
Effortlessly calculate the variance (Var[X]) of a discrete random variable online. Enter outcomes and probabilities for instant results and interactive visualizations.
Input Data
Enter comma-separated numerical outcomes.
Enter comma-separated probabilities for each outcome (sum must be 1).
Variance (Var[X]):
Probability Distribution Visualization
Understanding Discrete Variance
Variance measures how spread out a discrete random variable's possible values are. A higher variance indicates that the values are more spread out from the expected value (mean), while a lower variance suggests they are clustered closer to the mean.
For a discrete random variable X, the variance, denoted as Var(X) or σ2, is calculated using the formula: $$Var(X) = \sum_{i=1}^{n} (x_i - \mu)^2 P(x_i)$$, where:
- xi are the possible outcomes of X
- P(xi) is the probability of each outcome xi
- μ is the expected value (mean) of X, calculated as $$\mu = E[X] = \sum_{i=1}^{n} x_i P(x_i)$$
This calculator helps you quickly compute the variance by inputting the outcomes and their corresponding probabilities, providing a clear measure of data dispersion.
Learn more about variance and discrete random variables on resources like Wikipedia and introductory statistics textbooks.