Frequency Distribution Table Calculator: Formula, Worked Example and Free Online Tool

Published 31 October 2026 · By Sardar Zain, Founder of Orixiva · 13-minute read

A long list of raw numbers tells you very little. Thirty exam scores, two hundred delivery times or a thousand survey ages only start to make sense once you group them and count how many fall into each range. That grouped summary is a frequency distribution table, and a frequency distribution table calculator builds it for you without the tally marks, rounding mistakes or spreadsheet formulas.

This guide explains the frequency distribution formula step by step, works through a complete example by hand, shows how to read relative and cumulative frequency, and then walks you through the free Orixiva frequency distribution table calculator. It is a frequency distribution table calculator online without login, signin or signup, and it runs in your browser on a phone or computer.

What is a frequency distribution table?

Quick answer: A frequency distribution table lists groups of values (classes) next to the number of observations in each group (the frequency). It turns raw data into a summary that shows where values cluster, how spread out they are and whether the shape is symmetric or skewed.

There are two common types:

The Orixiva tool builds a grouped frequency table, because that is the version most people need for continuous data and the one that is slow to do by hand. For every class it reports the class range, midpoint, frequency (f), relative frequency, cumulative frequency and cumulative percentage, then highlights the modal class and draws a histogram.

The frequency distribution formula, step by step

There is no single “frequency distribution formula”. It is a short chain of formulas, each feeding the next. These are the exact rules the calculator uses.

Two checks catch most errors: the frequencies must add up to n, and the last cumulative percentage must be 100%.

Worked example: a frequency table for 30 exam scores

A teacher has these 30 test scores out of 100:

1. Count the values: n = 30.
2. Choose the classes: Sturges gives k = ⌈log₂ 30 + 1⌉ = ⌈5.91⌉ = 6.
3. Pick a tidy lower limit: the minimum is 42, so start at 40 to get round numbers.
4. Class width: (100 − 40) ÷ 6 = 10, giving 40–50, 50–60 … 90–100.
5. Count each class: each class includes its lower limit, so 70 goes in 70–80; the last class also includes the maximum, 100.
6. Add the percentages: divide each f by 30 and keep a running total.

Plotting the frequencies as touching bars gives a histogram. The orange line joining the midpoints is a frequency polygon. The shape rises to a peak in 70–80 and falls off slightly more slowly to the right.

Flowchart: building any frequency table

1. Collect the raw valuesOne number per observation; remove blanks and text
2. Are there only a few distinct values?
   YesUse an ungrouped table: one row per valueNoGroup the values into classes
3. Do you know how many classes you want?
   YesUse your k (5–15 is typical)NoUse Sturges: k = ⌈log₂ n + 1⌉
4. Width = (max − lower limit) ÷ kRound the lower limit down for tidy class edges
5. Tally f, then add relative and cumulative columnsf ÷ n, then running totals
6. Check Σf = n and the last cumulative % = 100%Then draw the histogram and describe the shape

How many classes should a frequency table have?

Too few classes hide the shape; too many leave lots of classes with zero or one value. Sturges’ rule is a sensible default for small and medium data sets, and it is what the calculator uses when you leave the number of classes at 0.

Other rules exist. The square-root rule uses k ≈ √n, and the Rice rule uses k ≈ 2·n^1/3; both give more classes than Sturges for large data sets. In practice, try the default, then increase or decrease the number of classes until the histogram shows a clear, readable shape. The Orixiva calculator accepts any whole number from 1 to 50.

Class limits, boundaries and where edge values go

The most common source of a wrong frequency table is a value sitting exactly on a class edge. Is a score of 70 in 60–70 or in 70–80? You need one consistent rule.

• Lower-inclusive rule (used by the calculator): each class includes its lower limit and excludes its upper limit, written [60, 70). A 70 goes into 70–80. The final class also includes the maximum, so nothing is left out.
• Textbook integer limits: some courses write 40–49, 50–59 for whole-number data. These are the same classes as [40, 50), [50, 60) for integers.
• Class boundaries: for 40–49, 50–59 the boundaries are 49.5 and 59.5. Histograms use boundaries so that the bars touch.

The tool lets you set the first class lower limit. Leave it blank to start at the minimum, or enter a round number (40 instead of 42) to get neater class edges. It must be less than or equal to the smallest value; otherwise the tool shows a clear error message.

How to read relative and cumulative frequency

The frequency column says “how many”. The other columns answer more useful questions:

Plotting the cumulative percentage against the upper class boundary gives an ogive. Read across from 50% to find the median, or from 25% and 75% to estimate the quartiles.

Grouped mean and median from a frequency table

When you only have the frequency table (for example from a published report), you can still estimate the average and the median.

For the exam scores, n/2 = 15, so the median class is 70–80 (the cumulative total passes 15 there). Median ≈ 70 + ((15 − 13) ÷ 8) × 10 = 72.5. The true median of the raw data is also 72.5.

The grouped mean is Σ(f × midpoint) ÷ n = (2×45 + 4×55 + 7×65 + 8×75 + 5×85 + 4×95) ÷ 30 = 2,170 ÷ 30 = 72.33. The true mean of the raw scores is 72.2. The small gap appears because grouping treats every value as if it sat at its class midpoint.

If you still have the raw data, use the Descriptive Statistics calculator in the same tool for the exact mean, median, standard deviation, quartiles and outliers.

How to use the free frequency distribution table calculator (step by step)

1. Open the calculator. Go to the Orixiva frequency distribution table calculator. It opens with sample data loaded. No login, signin or signup is needed.
2. Paste your data values. Separate numbers with commas, spaces, semicolons or new lines. You can paste a column straight from Excel or Google Sheets. At least 2 and up to 100,000 values are accepted.
3. Set the number of classes. Leave 0 to use Sturges’ rule, or enter your own number from 1 to 50.
4. Set the first class lower limit (optional). Leave it blank to start at the minimum, or enter a round number such as 0, 10 or 40.
5. Read the results. They update as you type: modal class, number of classes, class width, number of values and grouped mean, then the full table with midpoint, f, relative, cumulative and cumulative % columns, and a histogram.
6. Check the working. “How it was calculated” lists the class count rule, the width formula and how the relative and cumulative columns and the grouped mean were found.
7. Save or share. Copy the result, download it as a TXT file or print it. Press Calculate to keep it in Recent calculations and export that list as CSV.

Everything runs in your browser. Your numbers are not uploaded to a server, which matters when the data are student marks, patient readings or customer records.

Who uses a frequency distribution table calculator?

Frequency tables in Excel and Google Sheets

Spreadsheets can build a frequency table, but you have to create the class edges yourself. With data in A2:A31 and upper class limits in C2:C7:

Mistakes to avoid with frequency tables

Overlapping classes

Classes such as 40–50 and 50–60 must follow one edge rule, or a 50 gets counted twice or not at all.

Unequal class widths

Unequal widths distort a histogram because wide classes collect more values. Keep widths equal unless you are plotting frequency density.

Forgetting the total check

If Σf is not n, a value is missing or double-counted. The calculator shows n so you can compare it with your source.

Reading the modal class as the mode

The modal class is a range, not a single value. With the raw data, the mode can sit outside the modal class.

Treating the grouped mean as exact

The grouped mean is an estimate. Report the raw-data mean when you have the raw values.

For deeper background on histograms, relative histograms and cumulative histograms, the NIST/SEMATECH e-Handbook of Statistical Methods has a clear reference page.

Related guides: normal distribution calculator online, confidence interval calculator online, sample size calculator, t-test and p-value explained and how to calculate percentage.