Variance Calculator for Discrete Random Variable
Understand the spread of your data with this easy-to-use variance calculator.
Input Data
Enter the values of your discrete random variable and their corresponding probabilities, separated by commas.
Result
Variance (σ²):
Variance Calculation Breakdown
| Value (x) | Probability (P(x)) | x * P(x) | (x - E[x])² * P(x) |
|---|---|---|---|
| Total |
Understanding Variance
In probability theory and statistics, the variance of a discrete random variable is a measure of the spread of its possible values. A higher variance indicates that the values are more spread out around the mean (expected value).
The formula for the variance ($$ \sigma^2 = \sum_{i} (x_i - \mu)^2 P(x_i) $$) where:
- \( x_i \) are the possible values of the random variable.
- \( P(x_i) \) are the probabilities of these values.
- \( \\mu \) is the expected value (mean) of the random variable, calculated as $$ \mu = \sum_{i} x_i P(x_i) $$.
This calculator helps you quickly compute the variance by entering the values and their probabilities. Ensure that the sum of probabilities is approximately 1.
Learn more about variance on Wikipedia.