Frequency analysis is a statistical method used to describe how often values or categories occur in a set of data.
Despite its technical name, its main purpose is quite simple.
Frequency analysis helps you see how your data are distributed by counting the number of observations in each category or group.
Imagine you ask 80 students which teaching method they prefer:
| Teaching method | Frequency | % |
|---|---|---|
| Classroom | 28 | 35.0 |
| Online | 20 | 25.0 |
| Blended | 32 | 40.0 |
| Total | 80 | 100.0 |
The table immediately shows that:
Blended teaching is the most frequently selected method.
The basic purpose of frequency analysis is to organize a set of data so you can see how often each value or category occurs.
A frequency is simply the number of times something occurs.
The total frequency is 80 because 80 students took part.
Frequency is therefore a count.
A frequency can also be expressed as a percentage of the total.
For example, 28 of the 80 students prefer classroom teaching.
This represents 28 ÷ 80 × 100 = 35%.
So 35% of the students prefer classroom teaching.
Percentages are useful because they make the size of each group easier to understand and compare.
For example:
The percentages total 100%.
Frequency analysis can help you identify:
It provides a simple summary of the data before you carry out more complex statistical analyses.
A frequency distribution shows how observations are distributed among different values or categories.
The teaching-method example is a frequency distribution because it shows how the 80 students are distributed among three categories.
A frequency distribution can be presented in several ways, including:
A frequency table is particularly useful when you want to show exact frequencies and percentages.
Frequency analysis is commonly used with categorical data.
Categorical data place observations into different groups or categories.
Examples include:
Each student belongs to one of these categories.
You can then count the number of students in each category and calculate the percentage of the total.
Frequency analysis can also be used with numerical data.
Suppose you have the final examination scores of 80 students.
There may be many different individual scores, so it can be useful to group the scores into ranges.
For example:
| Examination score | Frequency | % | Cumulative % |
|---|---|---|---|
| 0–49 | 6 | 7.5 | 7.5 |
| 50–59 | 10 | 12.5 | 20.0 |
| 60–69 | 18 | 22.5 | 42.5 |
| 70–79 | 24 | 30.0 | 72.5 |
| 80–89 | 16 | 20.0 | 92.5 |
| 90–100 | 6 | 7.5 | 100.0 |
| Total | 80 | 100.0 |
This makes the overall pattern easier to see.
For example, the score range 70–79 contains the largest number of students.
Twenty-four students, or 30%, received a score within this range.
The examination-score example is a grouped frequency distribution.
Instead of showing every individual examination score, the scores have been placed into ranges.
For example:
Grouping can make a large set of numerical data easier to understand.
However, some detail is lost.
The table tells you that 24 students scored between 70 and 79, but it does not tell you their individual scores.
When the categories have a meaningful order, you can also calculate a cumulative frequency.
Cumulative means adding the frequencies as you move through the groups.
Using the examination-score example:
The cumulative frequency up to a score of 69 is therefore 6 + 10 + 18 = 34.
This means that 34 of the 80 students scored 69 or below.
The same information can be expressed as a cumulative percentage.
The percentages for the first three score ranges are:
Adding these figures ( 7.5 + 12.5 + 22.5 ) gives 42.5%.
This means that 42.5% of the students scored 69 or below.
Cumulative percentages are useful when you want to know the proportion of observations that fall at or below a particular value or group.
They are only meaningful when the categories have a natural order.
For example, examination-score ranges have an order because 60–69 comes before 70–79.
The teaching categories Classroom, Online, and Blended do not have a natural order, so a cumulative percentage would not normally be useful.
The value or category that occurs most often is called the mode.
In the teaching-method example:
Blended is therefore the modal category because it has the highest frequency.
For grouped numerical data, the group with the highest frequency is sometimes called the modal class.
In the examination-score example, 70–79 is the modal class because it contains the largest number of students.
This does not necessarily mean that one particular examination score within that range is the most common individual score.
You may also see the term relative frequency.
Frequency is the number of observations in a category.
Relative frequency expresses that number as a proportion of the total.
For example, 28 of the 80 students prefer classroom teaching.
The relative frequency is 28 ÷ 80 = .35.
This can also be expressed as 35%.
So frequency, relative frequency, and percentage describe related information in different forms:
Frequency analysis describes the data you have collected.
It does not by itself explain why the results occurred.
For example, 40% of the students prefer blended teaching.
Frequency analysis tells you how many students selected blended teaching, but it does not tell you why they prefer it.
It also does not by itself tell you whether:
Other statistical methods are used to answer these questions.
For example:
Frequency analysis is primarily used to describe the data.
A frequency table commonly includes some or all of the following information.
This identifies what is being counted.
For example:
For numerical data, it may contain individual values or groups of values such as 70–79.
Frequency shows the number of observations in each category or group.
For example, 32 students prefer blended teaching.
Percentage shows the frequency as a percentage of the total number of observations.
For example, 32 of 80 students represents 40%.
Cumulative percentage shows the running percentage as you move through ordered categories.
It is useful for ordered numerical data such as examination scores, ages, or income ranges.
It is generally not useful for categories that have no meaningful order.
For a small set of data, you can count the observations yourself.
For larger sets of data, spreadsheet or statistical software can calculate:
The software can also produce frequency tables and charts.
The important part is understanding what the results mean rather than performing the calculations by hand.
A basic frequency analysis describes the observations in your data.
It does not normally produce a p value or determine statistical significance.
For example, finding that 40% of the students prefer blended teaching describes the sample of 80 students.
It does not by itself establish that students more generally prefer blended teaching.
Additional statistical analysis would be required if you wanted to test a claim about a wider population or compare frequencies statistically.
Frequency analysis describes how often values or categories occur in a set of data.
A frequency is the number of observations in a category or group.
Percentages show each frequency as a proportion of the total.
Numerical data can be grouped into ranges to make the distribution easier to understand.
Cumulative frequencies and percentages show how observations accumulate across categories that have a meaningful order.
Frequency analysis can help you identify the most common and least common values and understand the overall distribution of the data.
It describes the data but does not by itself explain why a pattern occurs, establish cause and effect, or determine whether relationships or differences are statistically significant.
For examples showing how to present frequency results, see Frequency Table in APA Format.
When should I show frequency only, percentage only, or both?
Show frequency when the actual number of observations is important.
Show percentage when you want readers to compare the relative size of categories, particularly when the total number of observations may not be immediately obvious.
In many cases, showing both is most useful because readers can see both the number of observations and their proportion of the total.
For example, reporting that 32 students (40%) preferred blended teaching provides more information than either figure alone.
Can frequency analysis be used with non-numerical data?
Yes.
Frequency analysis is particularly useful for non-numerical categorical data such as:
You count how many observations fall into each category and, if useful, calculate the percentage in each category.
Should I include categories with a frequency of zero?
Sometimes.
If a category was part of the original data collection or response options, including it can show readers that the category was available but no observations fell into it.
For example, if students could choose Classroom, Online, Blended, or Other, and nobody chose Other, reporting a frequency of 0 may be useful.
If the category is irrelevant to the analysis, there is usually no need to add it simply to show a zero.
Should I combine categories that have very small frequencies?
Possibly, but only when combining them makes sense.
Very small categories can make a frequency table unnecessarily long or make comparisons difficult.
You might combine several related categories into an Other category.
However, do not combine categories simply to make the table look neater if doing so removes information that is important to the analysis.
What happens if some participants do not answer the question?
You need to decide what total the percentages are based on.
For example, suppose 80 students take part but only 76 answer a question about teaching preference.
You could calculate the percentages using the 76 students who answered rather than all 80 participants.
If missing responses affect how the percentages were calculated, explain this clearly in the table or accompanying text.
When should I use cumulative percentages?
Use cumulative percentages when the categories have a meaningful order and you want to show how observations accumulate across that order.
Examples include:
Do not normally use cumulative percentages for categories such as country of birth or teaching method because there is no meaningful order in which to accumulate them.
Can I compare frequencies between two groups?
Yes, but percentages are often more useful when the groups are different sizes.
Suppose 30 students in one group and 60 students in another prefer blended teaching.
The raw frequencies suggest a large difference, but the groups may contain different total numbers of students.
Comparing percentages allows you to take the different group sizes into account.
A statistical test may be needed if you want to determine whether an observed difference between groups is statistically significant.
Should percentages always total exactly 100%?
Not necessarily.
Percentages may total 99.9% or 100.1% because individual values have been rounded.
They may also total less than 100% if some responses are missing or if the table shows only selected categories.
Do not change correctly calculated percentages simply to force the total to equal exactly 100%.
Is frequency analysis enough to answer my research question?
That depends on the question.
Frequency analysis is useful when you want to describe how often values or categories occur.
If you want to examine relationships, make predictions, or test differences between groups, you will usually need another statistical method.
For example: