Frequency Distribution Calculator - Create Tables
Build a complete frequency distribution table from any dataset. Get class intervals, frequencies, relative frequencies, cumulative frequencies, and key summary statistics instantly.
Paste or type your numbers separated by commas or spaces, choose the number of class intervals, and click Calculate to generate the full frequency table and summary.
Frequency Distribution Calculator
Organise data into grouped class intervals with frequencies and statistics
Separate numbers with commas, spaces, or line breaks.
About the Frequency Distribution Calculator
A frequency distribution is a tabular summary that shows how often each value — or range of values — appears in a dataset. By organising raw data into a manageable number of class intervals and counting the observations in each interval, a frequency distribution table transforms an unordered list of numbers into a structured picture of the data's shape, centre, and spread. Frequency distributions are a foundational concept in descriptive statistics and form the basis for histograms, relative frequency polygons, and cumulative frequency curves.
A grouped frequency distribution divides the data's range into a fixed number of non-overlapping class intervals of equal width. Each interval has a lower bound, an upper bound, and a midpoint. The frequency is the count of data points that fall within the interval. The relative frequency is the frequency expressed as a proportion (or percentage) of the total count, making it easy to compare distributions across datasets of different sizes. The cumulative frequency is a running total of the frequencies from the first class to the current one, showing how many data points lie at or below each class boundary.
Choosing the number of classes is a balance: too few classes merge distinct patterns into a single lump, while too many classes spread data so thinly that no clear pattern emerges. A common heuristic is Sturges' rule: k = 1 + 3.322 × log₁₀(n), where n is the number of data points. For example, 20 data points suggest k ≈ 5 classes; 100 data points suggest k ≈ 7 classes. The class width is then width = (max − min) / k, rounded up to a convenient value to ensure all data points fit neatly.
The summary statistics derived from a frequency distribution are approximations based on the grouped data rather than the individual values. The grouped mean is calculated as Σ(midpoint × frequency) / n. The grouped standard deviation measures the spread of the data around the grouped mean. The grouped median is estimated by interpolation within the class interval containing the n/2-th observation. These approximations are very close to the exact values calculated from the raw data when the class width is small relative to the range.
Frequency distributions are used across every field that generates numerical data. Educators use them to analyse class test scores and identify students who may need extra support. Businesses analyse sales transaction amounts, product review ratings, or customer wait times to identify peaks and bottlenecks. Healthcare researchers distribute clinical measurements such as blood pressure, cholesterol, or BMI readings to understand population health. Quality-control engineers examine measurements from production processes to detect defects or drift. In each case, the frequency distribution table is the starting point for more advanced analysis.
Frequency Distribution — Examples
Three practical datasets showing different class structures and summary statistics.
| Dataset | Structure | Context |
|---|---|---|
| 82,90,75,68,88,75,95,100,72,85,91,78,84,88,77,95,65,80,73,86 — 5 classes | Classes: [65,72), [72,79), [79,86) … ; Mean ≈ 82.85 | Student test scores for a class of 20. Class width = 7. Most scores cluster in the 72–93 range with a slight left tail. |
| 150,220,180,190,250,160,200,210,170,240,195,175,215,185,230 — 6 classes | Classes: [150,170), [170,190), [190,210) … ; Mean ≈ 202.7 | Daily sales figures. Class width = 20. The distribution shows most days clustering in the $170–$230 range. |
| 35,42,38,50,45,48,36,39,47,41,43,46,40,37,44,49,38,42,45,36 — 5 classes | Classes: [35,38), [38,41), [41,44) … ; Mean ≈ 42.1 | Plant heights in cm from a botanical study. The bell-shaped distribution confirms a roughly normal growth pattern. |
How to use the Frequency Distribution Calculator
- Enter your numeric data in the 'Data Set' field. You can separate values with commas, spaces, or line breaks. The calculator accepts any mix of these delimiters.
- Choose the number of classes (bins) that best suits your dataset. A good starting point is 5 classes for small datasets (n < 30) and 7–10 for larger ones. You can use Sturges' rule: k ≈ 1 + 3.322 × log₁₀(n).
- Click 'Calculate'. The calculator finds the minimum and maximum, computes the class width as (max − min) / classes rounded up, and assigns each data point to the appropriate interval.
- Read the frequency table. Each row shows the class interval, midpoint, frequency count, relative frequency (as a percentage of total), and cumulative frequency (running total).
- Check the summary statistics below the table for the grouped mean, median, standard deviation, and class width. Use the load-example buttons to try the calculator with pre-filled datasets.
Frequency Distribution Calculator — FAQ
What is a frequency distribution table?
A frequency distribution table organises raw numerical data into groups called class intervals (or bins) and counts how many values fall in each group. It transforms an unordered list into a structured summary showing where data points cluster, how spread out they are, and what the overall shape of the distribution looks like.
How do I choose the number of classes?
A common approach is Sturges' rule: k = 1 + 3.322 × log₁₀(n), where n is the sample size. This gives about 5 classes for 20 data points and about 7 for 100. Alternatively, just experiment: start with 5 classes and increase until the distribution reveals a clear pattern without becoming too noisy. Most textbooks recommend 5–15 classes.
What is relative frequency and why is it useful?
Relative frequency is the proportion of total observations that fall in a class: relative frequency = class frequency / total n. It converts counts to percentages, making it easy to compare distributions from datasets of different sizes. For example, knowing that 35% of exam scores fall in the 70–80 range is more informative than knowing the count when comparing two classes of different sizes.
What is cumulative frequency?
Cumulative frequency is the running total of frequencies from the first class to the current one. It tells you how many data points lie at or below the upper boundary of each class. For example, if the cumulative frequency at the end of the third class is 15 out of 20, then 75% of observations fall in the first three classes. Cumulative frequency is the basis for the ogive (cumulative frequency curve).
Why are the mean and standard deviation labelled 'grouped'?
When data is grouped into class intervals, you lose the exact individual values. The grouped mean and standard deviation are computed using the midpoint of each class as a representative value, which introduces a small approximation. These estimates are very accurate when the class width is small relative to the range, but may differ slightly from statistics computed on the exact raw data.
What is the difference between frequency and relative frequency histograms?
A frequency histogram plots the raw count on the y-axis, while a relative frequency histogram plots the proportion (or percentage). Relative frequency histograms are directly comparable across datasets of different sizes and can be used as empirical approximations of the underlying probability distribution. The shape is identical in both cases — only the scale of the y-axis changes.