Frequency Table
A frequency table is a table that shows each value (or group of values) in a data set alongside the number of times it appears. It organizes raw data so you can quickly see which values are most and least common.
A frequency table is a statistical tool that summarizes data by listing distinct values or class intervals in one column and their corresponding frequencies — the count of observations falling within each category — in an adjacent column. When data is grouped into intervals (also called bins or classes), the result is a grouped frequency table. A relative frequency column may also be included, showing each frequency as a fraction or percentage of the total.
Example
Problem: A teacher recorded the scores of 20 students on a quiz (out of 5): 3, 5, 4, 2, 3, 4, 4, 5, 3, 3, 2, 4, 5, 3, 4, 3, 2, 4, 5, 3. Build a frequency table for this data.
Step 1: List each distinct score in order from lowest to highest: 2, 3, 4, 5.
Step 2: Go through the data and tally how many times each score appears. Score 2 appears 3 times, score 3 appears 7 times, score 4 appears 6 times, and score 5 appears 4 times.
Step 3: Check that the frequencies add up to the total number of data values.
Step 4: Write the completed table with columns for Score and Frequency: Score 2 → 3, Score 3 → 7, Score 4 → 6, Score 5 → 4.
Answer: The frequency table shows that a score of 3 was most common (7 students) and a score of 2 was least common (3 students).
Visualization
Why It Matters
Frequency tables are one of the first steps in analyzing any data set. Journalists use them to summarize survey results, scientists use them to spot patterns in experimental data, and businesses use them to track things like the number of customer orders per day. They also serve as the foundation for building histograms, bar charts, and other statistical graphs.
Common Mistakes
Mistake: Frequencies don't add up to the total number of data values
Correction: Always check that the sum of all frequencies equals the total count of observations. If it doesn't, you've either missed a data point or counted one twice.
Mistake: Using overlapping intervals in a grouped frequency table
Correction: Intervals must not overlap, or a value could be counted in two groups. For example, use 1–10 and 11–20, not 1–10 and 10–20, since 10 would belong to both.