# Histogram

From Open Risk Manual

## Definition

A **Histogram** is a numerical approximation (and associated visual depiction) of the observed (sampled) distribution of a continuous Random Variable after its range has been suitably decomposed into a numbef of bins. The bins are typically consecutive and non-overlapping intervals of a variable.

## Formula

If is the set of N observed values, k is the number of distinct bins, and are the left and right boundaries of the i-th bin, then the histogram is the function that counts how many observations fall into each bin.

Hence the sum