Frequency Distribution Table Calculator
Turn a list of numbers or categories into a frequency distribution table — class limits and boundaries, midpoints, frequencies, relative frequencies and both cumulative columns. Let Sturges' rule choose the number of classes or set the class width yourself, then copy the table as CSV or Markdown.
0 values detected
Leave blank for Sturges' rule: 1 class for 0 values.
Enter at least two values to build a frequency table.
How to Use the Frequency Distribution Table Calculator
- 1. Choose the type of data. Numbers for measurements and scores; categories for labels such as "Bus" or "Agree", one per line or separated by commas.
- 2. Paste the data. The count under the box tells you how many values were read.
- 3. Pick the table. For numbers, a grouped table sorts values into class intervals and an ungrouped table gives each distinct value its own row. For grouped tables, leave the number of classes blank to use Sturges' rule, or set the class width and a round starting value.
- 4. Copy the result. Copy as CSV for a spreadsheet or as Markdown for notes and documents.
How a Grouped Frequency Table Is Built
The example data are 30 quiz scores out of 50, ranging from 20 to 49. The calculator builds the grouped table in five steps — the same ones a textbook asks you to do by hand:
- Number of classes. Sturges' rule gives k = ⌈1 + log₂ n⌉ = ⌈1 + log₂ 30⌉ = ⌈5.91⌉ = 6 classes.
- Class width. Range ÷ k = (49 − 20) ÷ 6 ≈ 4.83, rounded up to the precision of the data: 5. If the division comes out exact, go one unit higher — otherwise the maximum would land just past the last class.
- Class limits. Start at the minimum (or a rounder number below it) and step by the width: 20–24, 25–29, 30–34, 35–39, 40–44, 45–49.
- Boundaries and midpoints. Boundaries sit half a unit outside the limits (19.5–24.5), so the classes meet without gaps. The midpoint is the average of the limits: 22 for the first class.
- Count. Tally each value into its class, then divide by n for the relative frequency and keep a running total for the cumulative columns.
| Class | Boundaries | Midpoint | Frequency | Relative (%) | Cumulative | Cumulative (%) |
|---|---|---|---|---|---|---|
| 20–24 | 19.5–24.5 | 22 | 2 | 6.67 | 2 | 6.67 |
| 25–29 | 24.5–29.5 | 27 | 2 | 6.67 | 4 | 13.33 |
| 30–34 | 29.5–34.5 | 32 | 4 | 13.33 | 8 | 26.67 |
| 35–39 | 34.5–39.5 | 37 | 8 | 26.67 | 16 | 53.33 |
| 40–44 | 39.5–44.5 | 42 | 9 | 30 | 25 | 83.33 |
| 45–49 | 44.5–49.5 | 47 | 5 | 16.67 | 30 | 100 |
Reading the Columns
- Frequency (f) is the count in each class. The column sums to n.
- Relative frequency is f ÷ n, shown as a percentage, so tables of different sizes compare directly. In the example, 30% of the scores fall between 40 and 44.
- Cumulative frequency is the running total: 16 students scored 39 or below. Cumulative relative frequency puts that as a share — 53.33% — and is what an ogive plots.
- Class boundaries are the edges a histogram's bars are drawn between. Midpoints stand in for every value in a class when you estimate statistics from grouped data: Σ(f × midpoint) ÷ n = 1135 ÷ 30 ≈ 37.83 here, close to the true mean of 37.9.
Choosing the Number of Classes
Too few classes hide the shape of the data; too many leave most classes holding one or two values. Most textbooks recommend between 5 and 20. Sturges' rule (1926) is the classic default and works well for small, roughly symmetric datasets, but it grows slowly — 1,000 values still get only 11 classes — so with large or skewed samples try more classes, or the square-root choice k ≈ √n.
Choosing the width directly is often cleaner. A width of 10 starting at 20 turns the quiz scores into the familiar grade bands 20–29, 30–39 and 40–49, with 4, 12 and 14 students. Whatever you choose, keep every class the same width — unequal widths distort a histogram — and make sure no value falls between two classes.
Frequently Asked Questions
- How do you make a frequency distribution table?
- Decide the number of classes, compute the class width as the range divided by the number of classes (rounded up), and list the class limits from the minimum upward. Then count how many values fall in each class. Relative frequency is each count divided by n, and cumulative frequency is the running total of the counts.
- What is the difference between class limits and class boundaries?
- Class limits are the smallest and largest values that can be recorded in a class, such as 20–24 for whole-number scores. Class boundaries split the gap between neighbouring classes — 19.5 and 24.5 — so the classes touch without gaps. Histograms are drawn on the boundaries.
- How do you find the class width?
- Divide the range (maximum minus minimum) by the number of classes and round up to the precision of your data. For scores from 20 to 49 in six classes, 29 ÷ 6 ≈ 4.83, so the width is 5. If the division is exact, add one unit so the maximum value still fits in the last class.
- What is relative frequency?
- Relative frequency is the proportion of all observations that fall in a class: its frequency divided by the total count. It is usually written as a percentage, and the relative frequencies of all classes add up to 100% (allowing for rounding).
- What is cumulative frequency used for?
- Cumulative frequency tells you how many observations fall at or below the upper boundary of each class. It is what you need to find medians, quartiles and percentiles from grouped data, and plotted against the upper boundaries it gives an ogive.
- Can I make a frequency table for words or categories?
- Yes. Switch the data type to categories and paste one label per line or separated by commas. Each distinct label gets a row with its frequency and percentage, and you can order the rows by first appearance, alphabetically or by frequency. Cumulative columns only mean something when the categories have a natural order, like survey responses from "Strongly disagree" to "Strongly agree".