Build grouped and ungrouped frequency distribution tables with histograms, cumulative frequencies, relative frequencies, and class count rule comparison.
The frequency distribution calculator organizes raw data into a structured frequency table — both grouped (with class intervals) and ungrouped (individual values). It automatically determines the optimal number of classes using Sturges' rule, or lets you choose the square root method or a custom count.
For each class, the calculator computes absolute frequency, relative frequency, cumulative frequency, and cumulative relative frequency. It generates an inline histogram visualization, displays the ogive (cumulative frequency) data, and compares three standard class-count rules side by side.
Enter your raw data, select a class-count method, and get a publication-quality frequency distribution with every metric needed for reports, homework, or data exploration. Check the example with realistic values before reporting. Use the steps shown to verify rounding and units. Cross-check this output using a known reference case. Use the example pattern when troubleshooting unexpected results. Validate that outputs match your chosen standards. Run at least one manual sanity check before publishing.
Frequency distributions are the foundation of data description and visualization. This calculator automates the tedious process of sorting, counting, and organizing data into classes, while providing every metric (relative frequency, cumulative frequency, class width, ogive data) needed for comprehensive statistical analysis.
From homework problems to professional reports, the frequency distribution table — paired with its histogram — is the first tool you reach for when exploring a new dataset.
Sturges' Rule: k = 1 + 3.322 log₁₀(n). Square Root: k = √n. Rice Rule: k = 2n^(1/3). Class width = Range / k (rounded up). Relative frequency = class frequency / n. Cumulative frequency = running total.
Result: 5 classes, width 6.0, most frequent class: [73, 79) with 3 values
With 15 values, Sturges' rule gives k = 5 classes. Range = 95 − 67 = 28, class width = 6. The classes span from 67 to 97, with the most populated class containing 3 values (20% of data).
A frequency distribution transforms a list of numbers into a structured summary. By grouping values into classes and counting occurrences, patterns emerge: the center of the distribution, its spread, and its shape (symmetric, skewed, bimodal). Every histogram, density plot, and CDF starts with frequency distribution as the underlying computation.
Class width affects what the histogram reveals. Too narrow (many classes) and the histogram becomes spiky noise. Too wide (few classes) and important structure disappears. Sturges' rule assumes normality; the Freedman-Diaconis rule (width = 2 × IQR × n^{-1/3}) adapts to the data's actual spread and is more robust for skewed distributions.
In manufacturing, frequency distributions of measurements reveal whether a process is centered on target, how much variation exists, and whether the distribution is normal. Control charts and process capability indices (Cp, Cpk) are computed from frequency distribution parameters. SPC (Statistical Process Control) begins with understanding the frequency distribution.
A frequency distribution organizes data by counting how many values fall into each category or class interval. It transforms raw, unstructured data into a summary table that reveals the distribution shape — where values concentrate, how they spread, and whether there are gaps or clusters.
Ungrouped frequency counts each unique value individually (e.g., "the value 72 appears 3 times"). Grouped frequency combines values into ranges/classes (e.g., "70–79 has 5 values"). Use ungrouped for discrete data with few unique values; use grouped for continuous data or many unique values.
Use Sturges' rule (1 + 3.322 log₁₀n) as a starting point. Adjust based on the resulting histogram: too few classes produce a flat, uninformative chart; too many make it spiky and noisy. For most practical work, 5–15 classes work well. Try different values and pick the one that best reveals the data's pattern.
Relative frequency is the proportion: class freq / total n. It tells you what fraction of data falls in each class. Cumulative frequency is the running total: how many values are at or below that class. Cumulative relative frequency at the last class should equal 100%.
An ogive (cumulative frequency polygon) plots cumulative frequency against the upper class boundary. It's an S-shaped curve for normal data. You can read approximate percentiles directly from the ogive: find 50% on the y-axis and read the corresponding x-value for the median.
This calculator is designed for numerical (quantitative) data. For categorical data (colors, types, labels), a simple tally count works — you don't need class intervals or cumulative frequencies. Use a bar chart for categorical data visualization.