Frequency Distribution Calculator — Histogram & Class Frequencies

Formula

How this is calculated

A grouped frequency distribution organises a large data set into a smaller number of equal-width intervals called classes or bins, making it easy to see the shape of the distribution at a glance. The calculator first finds the minimum and maximum of your data to determine the range, then divides the range by the number of classes k to get the class width. Class boundaries are computed as: class i runs from min + (i − 1) × width to min + i × width, with the last class being closed on both ends to capture the maximum value.

Each data value is assigned to the class whose lower boundary is ≤ value < upper boundary. The count for each class is tallied, the relative frequency is the count as a percentage of total observations n, and the cumulative frequency is the running sum of counts from the first class through that class. The modal class is the one with the highest count.

Choosing k: a common rule of thumb is Sturges' formula k ≈ 1 + 3.32 × log₁₀(n), which gives roughly 4–8 classes for most data sets up to a few hundred points. For very skewed distributions or smaller data sets, fewer classes may show the shape more clearly; for large data sets more classes reveal more detail. Equal class widths are used throughout — this calculator does not support unequal widths.