A cumulative distribution function (CDF) is a statistical tool that maps a value to its cumulative probability. Specifically, the CDF of a random variable (X) gives the probability that (X) will take a value less than or equal to a specific value (x). This function is defined for both discrete and continuous random variables, making it versatile in statistical analysis.

The CDF is always non-decreasing, meaning that as you move to higher values of (x), the cumulative probability either increases or remains the same. For example, if you have a sample of values, you can compute the CDF by determining the fraction of values that are less than or equal to (x). This can be particularly useful for understanding the distribution of data and identifying percentiles, such as the median or quartiles ²⁵.

In practice, CDFs help visualize the distribution of data and can be used to compare different datasets effectively.