# Frequency Distribution Calculator

Free frequency distribution calculator. Determine class width, boundaries, and expected frequencies for grouped data.

## What this calculates

Group your data into frequency distribution classes. Enter the range of your data and desired number of classes to get class widths, boundaries, and expected frequencies for histogram construction.

## Inputs

- **Number of Data Points** — min 1 — Total number of data points in your dataset.
- **Minimum Value** — The smallest value in your dataset.
- **Maximum Value** — The largest value in your dataset.
- **Number of Classes** — min 2, max 20 — Number of class intervals (typically 5-20).

## Outputs

- **Class Width** — Width of each class interval.
- **Class Boundaries** — formatted as text — Lower and upper boundaries for each class.
- **Expected Frequency per Class** — Average expected frequency if data were uniformly distributed.
- **Range** — Difference between max and min values.
- **Sturges' Rule Suggestion** — Suggested number of classes using Sturges' formula.

## Details

A frequency distribution organizes raw data into classes (intervals), making it easier to see patterns and construct histograms.

Key concepts: The class width is calculated as (max - min) / number of classes, rounded up for clean boundaries. Each class covers an equal interval, and every data point falls into exactly one class. The expected frequency per class (assuming uniform distribution) is n / k, where n is the number of data points and k is the number of classes.

Choosing the right number of classes: Too few classes hides the shape of the distribution; too many makes it noisy. Sturges' rule (k = 1 + 3.322 x log10(n)) is a common guideline. For 50 data points, it suggests about 7 classes. The square root rule (k = sqrt(n)) is another popular choice.

## Frequently Asked Questions

**Q: How do I choose the number of classes?**

A: Sturges' rule (k = 1 + 3.322 x log10(n)) works well for roughly normal data. The square root rule (k = sqrt(n)) is simpler. For most datasets with 20-200 data points, 5-12 classes work well. Adjust based on the shape of your data.

**Q: What is the difference between class limits and class boundaries?**

A: Class limits are the stated endpoints (e.g., 10-19). Class boundaries add 0.5 units to eliminate gaps between consecutive classes (e.g., 9.5-19.5). Boundaries ensure every possible value falls into a class with no gaps.

**Q: Can classes have different widths?**

A: Yes, unequal class widths are sometimes used (e.g., for income data with long tails), but equal widths are standard. With unequal widths, you must use frequency density (frequency / width) instead of frequency for the histogram y-axis.

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Source: https://vastcalc.com/calculators/statistics/frequency-distribution
Category: Statistics
Last updated: 2026-04-21