Standard Deviation Calculator for Discrete Random Variables
Easily calculate the standard deviation of a discrete random variable online. Enter values and probabilities to find the spread of your probability distribution.
Input Values and Probabilities
Standard Deviation:
Understanding Standard Deviation
Standard deviation measures the dispersion or spread of a set of values. A low standard deviation indicates that the values tend to be close to the mean (average), while a high standard deviation indicates that the values are spread out over a wider range. For a discrete random variable, standard deviation (σ) is calculated using the formula:
- xᵢ represents each value of the discrete random variable.
- P(xᵢ) is the probability of each value xᵢ.
- μ is the mean of the discrete random variable, calculated as $$ \mu = \sum_{i=1}^{n} x_i P(x_i) $$.
This calculator helps you quickly determine how much your discrete data points deviate from the average, providing valuable insights into the distribution. Use it to analyze datasets where outcomes are distinct and countable, each with an associated probability.