Variance Calculator for Discrete Random Variable
Easily calculate the variance of a discrete random variable online. Input values and probabilities to find the variance and understand data spread.
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.