Frequency Table: Definition, Types, Examples, and How to Create One

Learn how a frequency table turns raw observations into clear counts, proportions, percentages, and cumulative totals, with formulas and worked examples you can follow step by step.

Absolute and relative frequency   •   Cumulative frequency   •   Worked examples

 

What is a frequency table?

A frequency table organizes data by showing how many observations fall into each value or category. In statistics, the word frequency means the number of times something appears. The table converts a long, untidy list of responses into a compact summary that is easier to read and compare.

Suppose ten students report how many days they exercised last week:

2, 3, 1, 4, 3, 2, 5, 3, 2, 4

Reading the raw list tells you every answer, but the pattern is not immediately clear. Counting the values shows that one student exercised for one day, three exercised for two days, three exercised for three days, two exercised for four days, and one exercised for five days. That organized summary is a frequency distribution.

The phrase frequency distribution refers broadly to the way observations are spread across values or categories. A frequency table is one of the most common ways to display that distribution. For categorical variables, the rows usually contain category names. For numerical variables, they may contain individual numbers or grouped class intervals.

Why frequency tables are useful

Raw data preserves every observation, but it can hide the overall shape of the results. A frequency table reduces that complexity without changing the counts. It is often one of the first summaries created during descriptive data analysis.

 

A table does not explain why a pattern exists. It describes what was observed. Any explanation of causes requires additional evidence, a suitable research design, and careful analysis.

Main parts of a frequency table

A simple table may need only a category column and a count column. More detailed tables add proportions, percentages, and cumulative totals. These four components cover most introductory frequency-table tasks.

 

Absolute frequency

Absolute frequency is the direct count of observations in a category. It is usually written as f. If seven students prefer the quiet study room, the absolute frequency for that response is 7.

 

Imagine that 12 people choose a preferred study location. Five choose the library, four choose home, two choose a cafe, and one chooses an outdoor space. The absolute frequencies are 5, 4, 2, and 1. Their total must equal the number of people who answered: 12.

 

Relative frequency and percentage frequency

Relative frequency expresses a category as a proportion of the total. Divide the category frequency by the total number of observations. A relative frequency can be written as a decimal, fraction, or percentage.

 

 

In the study-location example, 5 of 12 people chose the library. The relative frequency is 5 ÷ 12 = 0.4167. Multiplying by 100 gives 41.67%, usually reported as 41.7% when rounded to one decimal place.

All relative frequencies should total approximately 1. All percentage frequencies should total approximately 100%. A displayed total of 99.9% or 100.1% can occur when each row is rounded separately.

Basic frequency table for preferred study location

 

Cumulative frequency

Cumulative frequency is a running total. Start with the first frequency, then add each new row to the total from the rows above it. The last cumulative frequency must equal the total number of observations included in the table.

 

Cumulative frequency is meaningful only when the rows have a logical order. It works well for age, income bands, number of books read, satisfaction ranks, and class intervals. It is normally not useful for unordered nominal categories such as eye color or country of birth.

For example, if 2 students read no books, 4 read one book, and 7 read two books, the cumulative frequencies are 2, 6, and 13. The value 13 means that 13 students read two books or fewer.

Cumulative percentage applies the same idea to percentages. It shows the percentage of cases at or below the current ordered value or class.

Valid percentage and missing values

Survey and research data often contains unanswered questions, unreadable entries, or values coded as missing. A frequency table may therefore report both percentage and valid percentage.

Percentage uses every case in the sample as its denominator, including missing cases. Valid percentage uses only the cases that supplied an acceptable response.

 

 

Consider a survey of 20 students about their preferred library area. Two students skip the question, leaving 18 valid responses. Seven choose the quiet room. Its overall percentage is 7 ÷ 20 × 100 = 35.0%. Its valid percentage is 7 ÷ 18 × 100 = 38.9%.

Frequency table showing overall and valid percentages for a survey with two missing responses

 

 

How to create a frequency table step by step

The exact layout depends on the variable, but the following process works for most basic frequency tables.

1. Define the variable. State clearly what was measured and whether it is categorical, discrete numerical, or continuous numerical data.

2. Review and clean the observations. Check spelling, category labels, impossible values, duplicates, and missing-response codes.

3. List unique values or create class intervals. Use individual categories for categorical data. Group continuous data when the number of distinct values would make the table too long.

4. Tally each observation. Place every valid observation into one and only one row.

5. Count absolute frequencies. Convert the tally marks into numerical counts.

6. Calculate relative frequencies or percentages. Divide each count by the correct total and apply consistent rounding.

7. Add valid or cumulative columns when appropriate. Use valid percentages for missing data and cumulative totals only for ordered rows.

8. Add totals. The frequency total should equal the number of included observations.

9. Check the calculations. Relative frequencies should total about 1, percentages about 100%, and the final cumulative frequency should match the sample size.

10. Select a suitable chart. Match the chart to the variable and the purpose of the analysis.

COMPLETE WORKED EXAMPLE

Books read by 20 students

A teacher records the number of books each student read during one month:

0, 1, 2, 2, 3, 1, 4, 2, 3, 2, 1, 5, 0, 2, 4, 3, 2, 1, 3, 2

 

Step 1: Tally the observations

Count each value once. The frequencies are 2 students for zero books, 4 for one book, 7 for two books, 4 for three books, 2 for four books, and 1 for five books.

Step 2: Calculate the proportions and running totals

Divide each frequency by 20. For example, the relative frequency for three books is 4 ÷ 20 = 0.20, which equals 20%. Add the frequencies from top to bottom to obtain the cumulative column.

Complete frequency distribution for books read by 20 students

 

The table shows that 35% of students read two books. It also shows that 13 of 20 students, or 65%, read no more than two books. These are descriptive statements about the recorded month. They do not explain what caused the reading pattern.

Grouped frequency table for numerical data

A dataset with many distinct numerical values can produce an unnecessarily long table. A grouped frequency table solves this problem by placing values into non-overlapping class intervals.

Suppose commute times are recorded for 24 people:

4, 7, 9, 11, 13, 14, 16, 18, 19, 20, 22, 23, 24, 25, 26, 28, 29, 31, 34, 36, 39, 42, 47, 55

Terms used in grouped tables

 

 

For the whole-minute intervals below, the first class has boundaries of −0.5 and 9.5, so its width is 10 minutes. Each observation fits into exactly one interval.

Grouped frequency distribution for commute times of 24 people

 

The most common interval is 20–29 minutes, containing 8 people. The cumulative column shows that 17 of 24 people had a commute shorter than 30 minutes.

 

Frequency table vs frequency distribution

The terms are often used together, and many introductory texts use them almost interchangeably. A frequency distribution is the pattern of frequencies across the possible categories or values. A frequency table is a tabular format used to display that distribution.

The same distribution can also be represented graphically. A list of class frequencies, a histogram, and a frequency polygon may all describe the same underlying data from different visual perspectives.

Which chart should accompany a frequency table?

The best chart depends on the type of variable and the question you want the display to answer.

Chart selection guide

 

Frequency table in APA style

APA-style presentation aims to make a table understandable without unnecessary decoration. Requirements can vary by course, journal, institution, and edition, so always check the guidance that applies to your work.

 

A well-designed statistical table should make the meaning of every row, column, total, and denominator clear. Style is useful only when it supports accurate interpretation.

Common mistakes to avoid

1. Using overlapping class intervals. Classes such as 10–20 and 20–30 both contain 20. Use clearly exclusive intervals so every observation has one location.

2. Ignoring missing values. Report how many cases are missing and make the denominator for each percentage clear.

3. Dividing by the wrong total. Overall percentages use the full sample; valid percentages use non-missing responses.

4. Confusing counts with percentages. A frequency of 12 is not 12% unless the sample contains exactly 100 observations.

5. Forcing rounded percentages to equal 100. Small differences can result from rounding. Report a note rather than altering correct values without explanation.

6. Using cumulative frequency for unordered data. A running total has no natural interpretation when nominal categories can be rearranged freely.

7. Omitting a total row. Totals provide a fast check that all observations were counted and the denominator is visible.

8. Choosing too many or too few classes. Poor grouping can either fragment the pattern or conceal it.

9. Choosing the wrong chart. A histogram is intended for numerical intervals, while a bar chart is generally better for separate categories.

How to interpret a frequency table

Begin with the total number of valid observations. Then inspect the frequencies, proportions, and order of the rows. A careful reading usually considers several features:

·       Modal category or value: the row with the highest frequency.

·       Concentration: whether observations cluster in one or two rows.

·       Spread: how widely numerical values are distributed across the range.

·       Rare categories: rows with very small counts that may require cautious interpretation.

·       Empty classes: intervals with no observations, which can reveal gaps in numerical data.

·       Shape: whether a numerical distribution appears balanced, skewed, or concentrated at one end.

·       Missing responses: whether nonresponse is large enough to affect conclusions.

·       Overall versus valid percentages: whether excluding missing cases changes the apparent distribution.

Interpret the table in context. A category with 60% may look dominant, but the strength of that conclusion depends on the sample size, how participants were selected, how the question was worded, and how much data is missing.

Frequently asked questions

What is a frequency table?

A frequency table lists each value, category, or class interval in a dataset and shows how many observations belong to each one. It may also include proportions, percentages, and cumulative totals.

What is the difference between absolute and relative frequency?

Absolute frequency is the number of times a value occurs. Relative frequency divides that count by the total number of observations, so it expresses the category as a proportion of the dataset.

How do you calculate percentage frequency?

Divide the category frequency by the total number of observations and multiply the result by 100. For example, 8 cases out of 40 equal 20%.

What is cumulative frequency?

Cumulative frequency is a running total of frequencies from the first ordered value or class through the current row. It is useful for answering questions such as how many observations fall at or below a limit.

What is valid percentage?

Valid percentage is calculated using only observations with non-missing responses. Missing cases are excluded from its denominator.

Can a frequency table be used for continuous data?

Yes. Continuous values are commonly grouped into non-overlapping class intervals before their frequencies are counted.

What is the difference between a frequency table and a histogram?

A frequency table presents counts in rows and columns. A histogram displays a numerical frequency distribution with adjoining bars representing class intervals.

Should percentages always add to exactly 100%?

They should represent 100% of the relevant cases, but displayed values may total 99.9% or 100.1% because individual percentages have been rounded.