Frequency Distribution — Definition, Formula & Examples
A frequency distribution is a summary that shows how often each value (or range of values) occurs in a data set. It organizes raw data so you can quickly see which outcomes are common and which are rare.
A frequency distribution is a tabular or graphical arrangement that pairs each distinct value or class interval of a variable with its corresponding frequency — the count of observations falling within that category.
How It Works
Start by listing every distinct value or grouping values into equal-width intervals (called classes or bins). Then tally how many data points fall into each value or interval. Record these counts in a table with one column for the values/intervals and another for their frequencies. The resulting table reveals the shape of the data: where values cluster, where gaps exist, and whether the distribution is symmetric or skewed.
Worked Example
Problem: A teacher records quiz scores (out of 10) for 15 students: 6, 7, 8, 7, 9, 8, 8, 10, 7, 6, 9, 8, 7, 10, 9. Build a frequency distribution.
List distinct values: The scores that appear are 6, 7, 8, 9, and 10.
Count each value: Go through the data and tally each score.
Verify: Check that the frequencies sum to the total number of data points.
Answer: The frequency distribution is: Score 6 → 2, Score 7 → 4, Score 8 → 4, Score 9 → 3, Score 10 → 2. Scores of 7 and 8 are the most common.
Visualization
Why It Matters
Frequency distributions are the first step in almost every statistical analysis — you need to see the shape of your data before choosing measures of center or spread. In AP Statistics, psychology research, and quality control, building a frequency distribution is how you move from a messy list of numbers to meaningful patterns.
Common Mistakes
Mistake: Using class intervals of unequal width, which distorts comparisons between groups.
Correction: Keep all intervals the same width (e.g., 0–9, 10–19, 20–29) so that frequencies across intervals are directly comparable.