Frequency Table Calculator

How to Use the Frequency Table Calculator

This calculator creates ungrouped and grouped frequency distribution tables directly from raw data. The steps depend on the type of frequency table you want to create.

1. Ungrouped Table

Use an ungrouped frequency table when you want to list each distinct value or category separately. This option works with both numerical data and text or categorical data and is most useful when the dataset contains a manageable number of distinct values or categories.

For example, you can use it with numerical data such as: 1, 2, 2, 3, 4, 2, 1, or with text responses such as: Online, Hybrid, In-person, Online, Hybrid

To create an ungrouped frequency table using the calculator:

1. Enter or paste your observations into the Data field.
2. Select Ungrouped.
3. Choose the number of decimal places you want to display.
4. Click Calculate.

The calculator returns the frequency, relative frequency, percentage, cumulative frequency, and cumulative percentage for each distinct value or category.

For numerical data, the calculator arranges the values from smallest to largest before calculating cumulative frequencies. However, for text or categorical data, the categories follow the order in which they first appear in your dataset. The cumulative frequency and cumulative percentage therefore follow that same order.

Tip. Whether you use the cumulative columns depends on the type of categorical variable you are analyzing. They can be useful for ordered categories such as education level, age group, income bracket, satisfaction level, or Likert-scale responses. For categories with no meaningful order, such as preferred learning mode or favorite color, you may simply ignore the cumulative columns when reporting your results.

Grouped Table

Use a grouped frequency table when you have numerical data with many different values and want to combine them into class intervals.

For example, instead of listing every individual test score separately, you may want to group the scores into intervals such as: 50–59, 60–69, 70–79, 80–89

Grouped mode only accepts numerical data.

To create a grouped frequency table using the calculator:

1. Enter or paste your numerical data into the Data field.
2. Select Grouped.
3. Choose Number of Classes if you know how many intervals you want to create, or select Class Width if you know the width of each interval.
4. Enter the number of classes or class width.
5. Choose the number of decimal places you want to display.
6. Click Calculate.

The calculator instantly creates the class intervals and returns the class midpoint, frequency, relative frequency, percentage, cumulative frequency, and cumulative percentage for each class.

After creating either type of frequency table, click Copy Table to copy the completed table into Word or another document. You can also select Download CSV to save the table for Excel, Google Sheets, or another spreadsheet program.

What Is a Frequency Table?

A frequency table organizes data by showing how many times each value, category, or class interval occurs. The number of times something occurs is called its frequency, usually represented by (f).

Suppose the data are: 4, 5, 5, 6, 6, 6, 7. Instead of reading through the original values, we can summarize them as follows:

The table immediately shows that 6 occurs most often.

Frequency tables become especially useful when a dataset contains repeated observations or when you need to summarize many numerical values using class intervals.

Ungrouped vs Grouped Frequency Tables

Frequency tables generally fall into two types: ungrouped and grouped. The table below summarizes the main differences between grouped and ungrouped frequency tables.

Still struggling to determine which frequency table to use? Use an ungrouped frequency table when the number of distinct values is small enough to display clearly. However, if listing every individual value would make the table too long or difficult to interpret, use a grouped frequency table instead.

How to Create an Ungrouped Frequency Table Manually

Creating an ungrouped frequency table mainly involves identifying the distinct values and counting how many times each one occurs.

To create an ungrouped frequency table by hand:

1. List the distinct values. For numerical data, arrange them from smallest to largest.
2. Count the frequency of each value. Count how many times each value occurs in the dataset.
3. Calculate relative frequency. Divide each frequency by the total number of observations.
4. Convert the relative frequency to a percentage. Multiply the relative frequency by 100.
5. Find cumulative frequency if appropriate. Add the frequencies progressively from the smallest value upward.
6. Find cumulative percentage. Divide each cumulative frequency by the total number of observations and multiply by 100.

Example 1: Creating an Ungrouped Frequency Table

The following values show the number of online courses completed by 15 students:

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

Create an ungrouped frequency table.

Solution

To create a frequency table for the data, follow these steps:

Step 1: List the distinct values

The possible values are: 1, 2, 3, 4, 5

There are 15 observations. Hence, n = 15

Step 2: Count the frequency of each value

Count how many times each of the possible values appears.

• 1 appears 4 times.
• 2 appears 5 times.
• 3 appears 3 times.
• 4 appears 2 times.
• 5 appears 1 time.

The frequencies therefore are: 4, 5, 3, 2, 1

As a quick check: 4 + 5 + 3 + 2 + 1 = 15. Since the frequencies add to the total number of observations, the counts are correct.

Step 3: Calculate relative frequency

By definition, the relative frequency formula is: f/n, where f is the frequency and n is the total number of observations. For instance, for one completed course: Relative frequency = 4 / 15 = 0.2667. Similarly, for two completed courses, Relative frequency = 5 / 15 = 0.3333

Repeat the same calculation for the remaining values.

Step 4: Convert the relative frequencies to percentages

For one completed course: Percentage = 0.2667 × 100

= 26.67%

For two completed courses: Percentage = 0.3333 × 100

= 33.33%

You should repeat the same process for the remaining values.

Step 5: Calculate cumulative frequency

Start with the first frequency and add each subsequent frequency:

• First cumulative frequency = 4
• Second cumulative frequency = 4 + 5 = 9
• Third cumulative frequency = 9 + 3 = 12
• Fourth cumulative frequency = 12 + 2 = 14
• Fifth cumulative frequency = 14 + 1 = 15

The completed ungrouped frequency table is:

Therefore, two completed courses are the most common value, with a frequency of 5.

How to Create a Grouped Frequency Table Manually

A grouped frequency table takes a little more work because you first need to create suitable class intervals.

To create a grouped frequency table by hand:

1. Find the minimum and maximum values.
2. Choose the number of classes or class width.
3. Construct non-overlapping class intervals that cover the entire dataset.
4. Find the midpoint of each class.
5. Count how many observations fall into each interval.
6. Calculate relative frequency and percentage.
7. Calculate cumulative frequency and cumulative percentage.

For whole-number data, you can calculate a suitable class width using: Class width = (Highest value − Lowest value + 1) / Number of classes

Round the result up when necessary so that all observations fit within the classes.

However, for continuous or decimal data, class intervals should not overlap. For example, you might use:

• 10 ≤ x < 20
• 20 ≤ x < 30

This makes it clear where a value such as 20 belongs.

Example 2: Creating a Grouped Frequency Table

A researcher records the number of minutes taken by 20 participants to complete a task:

32, 35, 37, 39, 41, 43, 44, 46, 48, 50, 51, 53, 55, 57, 59, 61, 63, 65, 68, 70

Create a grouped frequency table using five classes.

Solution

To create a frequency table for the above data manually, follow these steps:

Step 1: Find the minimum and maximum values

• The smallest value is: Minimum = 32
• The largest value is: Maximum = 70

Step 2: Find the class width

Based on the data, five classes may be appropriate.

For whole-number data: Class width = (70 − 32 + 1) / 5

= 39 / 5

= 7.8

Round this value up: Class width = 8

Step 3: Create the class intervals

Starting at 32 and using a class width of 8 gives:

• 32–39
• 40–47
• 48–55
• 56–63
• 64–71

These five intervals cover every observation without overlap.

Step 4: Find the class midpoints

By definition, Midpoint = (Lower class limit + Upper class limit) / 2

For the first interval: Midpoint = (32 + 39) / 2

= 35.5

For the second interval: Midpoint = (40 + 47) / 2

= 43.5

Continue in the same way for the remaining classes.

Step 5: Count the frequency in each class

Now count how many observations fall in each interval.

• 32–39 contains 32, 35, 37, and 39, so f = 4.
• 40–47 contains 41, 43, 44, and 46, so f = 4.
• 48–55 contains 48, 50, 51, 53, and 55, so f = 5.
• 56–63 contains 57, 59, 61, and 63, so f = 4.
• 64–71 contains 65, 68, and 70, so f = 3.

Check the total: 4 + 4 + 5 + 4 + 3 = 20. The frequencies account for all 20 observations.

Step 6: Calculate the relative frequencies and percentages

For the first class: Relative frequency = 4 / 20

= 0.20

Percentage = 0.20 × 100

= 20%

For the third class: Relative frequency = 5 / 20

= 0.25

Percentage = 25%

You can do that for all the other classes.

Step 7: Calculate cumulative frequency

Add the frequencies from the first class downward:

• 4
• 4 + 4 = 8
• 8 + 5 = 13
• 13 + 4 = 17
• 17 + 3 = 20

The completed grouped frequency table is:

The 48–55 interval has the highest frequency, containing 5 of the 20 observations.

What Does Each Column in a Frequency Table Mean?

A frequency table can include several columns, depending on the type of data and the information you need. Here’s a quick summary of what each of the columns means.

• Frequency (f). It tells you how many times a value, category, or class occurs.
• Relative Frequency. It tells you what proportion of the entire dataset belongs to a particular value or class.
• Percentage Frequency. It expresses the relative frequency as a percentage.
• Cumulative Frequency. It gives a running total of the frequencies.
• Cumulative Percentage. It expresses the cumulative frequency as a percentage of the complete dataset.
• Class Midpoint. Grouped frequency tables often include a midpoint for each class. The midpoint formula is: Midpoint = (Lower class limit + Upper class limit) / 2

Number of Classes vs Class Width

When you select Grouped in the calculator, you can choose either Number of Classes or Class Width. Choose Number of Classes when the question tells you how many intervals to create. For example, “construct a grouped frequency distribution using six classes. In this case, select Number of Classes and enter 6.

However, if the problem specifies how wide each interval should be, choose Class Width. For example, if the question says “construct a grouped frequency distribution using a class width of 10,” you should select Class Width and enter 10.

The calculator will automatically determine how many intervals it needs to cover the data.

When Should You Group Data?

Group numerical data when there are so many distinct values that an ungrouped frequency table becomes difficult to read.

Suppose you measure the heights of 100 university students. You may have dozens of different heights. Listing each height separately would produce a long frequency table.

Grouping the measurements into intervals such as 150–159, 160–169, and 170–179 makes the overall distribution easier to see.

However, grouping also removes some detail because you can no longer see every exact observation from the table. If the dataset contains only a few distinct values, an ungrouped frequency table usually gives you more information.

Frequency Table vs Frequency Distribution

The terms frequency table and frequency distribution are closely related. A frequency distribution describes how observations are distributed across values, categories, or class intervals. On the other hand, a frequency table is the table used to display that distribution.

For this reason, our frequency table calculator can also be used as a frequency distribution calculator.

Frequency Table vs Bar Chart

A frequency table gives you the exact number or percentage of observations in each category. A bar chart presents the same type of information visually. For example, after creating a frequency table for student majors, you could plot the frequencies or percentages as bars.

If you want to visualize categorical or discrete frequencies, use our Bar Chart Maker.

Frequency Table vs Histogram

A histogram is mainly used to visualize the frequency distribution of numerical data grouped into intervals.

Unlike a bar chart, histogram bars normally touch because the intervals represent continuous numerical ranges. A grouped frequency table is often a useful first step before constructing a histogram.

If you want a visual representation of grouped numerical data, use the Histogram Maker.

Frequency Table vs Stem-and-Leaf Plot

A frequency table focuses on how often values or intervals occur. A stem-and-leaf plot shows the shape of a numerical distribution while preserving the individual observations.

For smaller numerical datasets, a Stem and Leaf Plot Calculator can be useful when you want to see the original values as well as the distribution.

Frequently Asked Questions