Histogram

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 $X_{j}$ is the set of N observed values, k is the number of distinct bins, and $B_{i}=[L_{i},R_{i}]$ 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.

$m_{i}=\sum _{j}^{N}1_{\{X_{j}\in B_{i}\}}$

Hence the sum

$N=\sum _{i}^{k}m_{i}$

See Also

• Wikipedia Entry
• Histogram versus Bar Plot