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