A frequency table is the first step in making sense of a pile of raw data. It counts how often each value, class or category occurs, then adds relative frequencies (shares of the total) and cumulative frequencies (running totals). This calculator builds the table from numbers, either grouped into class intervals or value by value, or from text responses such as survey answers, and draws a matching histogram or bar chart.
How to use the frequency table calculator
- Choose the data type: numbers in classes (a grouped table and histogram), each distinct number (a tally of exact values), or categories (text answers).
- Paste the data, separated by commas, spaces or new lines.
- For classes, enter a class width and a starting point, or leave both blank to let the calculator choose with Sturges’ rule.
- For categories, choose whether to ignore capitalization and how to sort the rows.
- Read the mode or modal class on the tape and the full table below the chart.
Frequency table formulas
For each class or category i with count fᵢ out of n observations:
When choosing classes automatically:
The grouped mean uses class midpoints mᵢ: x̄ ≈ Σ fᵢmᵢ ÷ n.
Worked example
A teacher records 25 exam scores: 62, 75, 81, 68, 90, 77, 73, 85, 58, 79, 88, 71, 66, 94, 83, 76, 70, 87, 64, 80, 72, 78, 91, 69, 84.
Using classes of width 10 starting at 50:
| Class | Frequency | Percent | Cumulative | Cumulative % |
|---|---|---|---|---|
| 50 – < 60 | 1 | 4% | 1 | 4% |
| 60 – < 70 | 5 | 20% | 6 | 24% |
| 70 – < 80 | 9 | 36% | 15 | 60% |
| 80 – < 90 | 7 | 28% | 22 | 88% |
| 90 – < 100 | 3 | 12% | 25 | 100% |
The modal class is 70 – < 80, with 36% of students. The cumulative column answers threshold questions directly: 24% scored below 70, and 88% scored below 90. Using midpoints, the grouped mean is (55 × 1 + 65 × 5 + 75 × 9 + 85 × 7 + 95 × 3) ÷ 25 = 77.4; the exact mean of the raw scores is 76.84.
Leaving width and start blank gives the same table here: Sturges’ rule suggests 6 classes, and the raw width of 6 rounds up to 10.
Reading the histogram
Shape
Look for where the bars peak, whether the distribution is symmetric or has a long tail to one side, and whether there are gaps or two separate peaks. The exam scores are roughly symmetric with a single peak in the 70s.
Class width changes the picture
The same data can look smooth or jagged depending on the width. If the shape changes dramatically when you try a neighboring width, the sample may be too small to say much about shape. For small data sets, a stem-and-leaf plot keeps every value visible.
Categorical data
For text categories the bars are separated, because the categories have no natural order or width. A frequency table of observed counts is also the input for a chi-square test of whether the categories occur in expected proportions. For exact summary statistics of numeric data, use the descriptive statistics calculator.
Frequently asked questions
How many classes should a frequency table have?
Usually 5 to 15. Sturges' rule, k = ⌈log₂ n⌉ + 1, is a common starting point: about 6 classes for 25 values and 11 for 1,000. Too few classes hide the shape of the data; too many leave most classes nearly empty. Choose a round class width so the boundaries are easy to read.
Which class does a value on a boundary go into?
This calculator uses left-closed classes: each class includes its lower limit and excludes its upper limit, so with classes 70–80 and 80–90, a value of 80 is counted in 80–90. Any consistent rule works, but state it so readers can reproduce the table.
What is the difference between relative and cumulative frequency?
Relative frequency is each class's share of the total (count ÷ n), so the relative frequencies add to 1 or 100%. Cumulative frequency is a running total from the first class down, so the last row equals n; cumulative percentages show how much of the data lies below each upper boundary.
Can I make a frequency table of words or categories?
Yes. Choose Categories (text), paste the responses separated by commas or new lines, and the calculator counts each distinct answer. You can ignore capitalization so that Blue and blue are counted together, and sort by frequency, alphabetically or by first appearance.
Why does the mean from classes differ from the actual mean?
A grouped mean assumes every value sits at its class midpoint. Values inside a class are rarely spread exactly evenly, so the estimate is slightly off. With raw data available, the exact mean from the descriptive statistics calculator is always better.