Frequency Distribution

What it does

Counts how many observations fall in each class or category, with relative and cumulative frequencies.

Use it to see where values concentrate, or to summarise a categorical variable.

Data you need

• One variable

Optional: Class count or class width

Supported data: Numeric, Categorical. Level: Beginner.

Formula and method

Relative frequency = f / n · Cumulative frequency = Σf

Numeric values are grouped into classes whose boundaries come from a rule such as Sturges or Freedman-Diaconis, or from a count or width you set. Each class includes its lower limit, and the last also includes its upper limit. Categories are counted directly.

How to read the result

Look for the classes holding the most observations and how quickly the cumulative percentage rises.

Worked example

Illustrative run on Simulated study data (teaching data). These figures are the actual output of this model on that example, and they say nothing about your own data.

• The most frequent class is [73.35, 78.7286) with 42 observations (17.5%).
• The table shows where observations concentrate and how quickly they accumulate.

Limitations

• Class boundaries change the picture

Numerical validation

Validated 17 of 17 automated checks passed, including numerical results, invalid input, missing values, small samples, constant variables, charts and the interpretation text.

Computed with python 3.13.2, numpy 2.2.5, scipy 1.14.1, pandas 2.3.3, statsmodels 0.14.4, scikit-learn 1.7.0, in your browser. A passing check confirms the listed comparison only. It does not make any result suitable for your data, and it is not a claim of equivalence with other statistical software.

Questions

How many classes should a histogram have?

There is no single right number. Automatic rules such as Sturges or Freedman-Diaconis are starting points; try a few widths before drawing conclusions about shape.