Frequency Distribution Calculator

A frequency distribution organizes raw data into groups called bins and counts how many observations land in each. It is the foundational step before almost any distributional analysis.

To build one: choose a bin count (Sturges’ rule gives 1 + 3.32 x log(n) as a rough estimate), divide the data range into equal-width intervals, then count. This calculator does that automatically.

The output table shows each interval, the raw count, and the relative frequency as a percentage. The last bin always includes its upper bound so no data points fall out.

Bin count matters more than most people realize. Too few bins crushes the distribution into a shapeless blob. Too many gives you one bar per value, which is noise. For datasets under 50 observations, 5 bins usually works. For 100-500 points, 8-12 is typical. For large samples (1000+), 15-20 can reveal subtle structure.

Worked example: data [5, 7, 8, 10, 12, 15, 15, 18, 20, 22], 4 bins, range 5-22, width = 4.25.

• Bin 1: [5.00, 9.25) -> count 3 (30%)
• Bin 2: [9.25, 13.50) -> count 2 (20%)
• Bin 3: [13.50, 17.75) -> count 3 (30%)
• Bin 4: [17.75, 22.00] -> count 2 (20%)

The histogram shows the shape at a glance. A symmetric mound suggests a normal-ish distribution. A long right tail means most values cluster low with a few large outliers. A flat histogram means values are spread evenly.

For continuous data, these are half-open intervals: [lower, upper) for every bin except the last, which is closed on both ends.