How to use the frequency distribution calculator
- Choose Each value to count how often every distinct value or word appears, or Grouped classes to put numbers into equal-width classes.
- Paste your values. Numbers can be separated by commas, spaces or new lines. Words must be separated by commas or new lines so that a phrase such as New York stays together.
- For classes, enter the class width and, if you like, where the first class starts. Each class includes its lower limit and stops just below the next one.
- Read the table: frequency, relative frequency as a percent, cumulative frequency and cumulative percent.
Formula
Frequency = how many values fall in the row
Relative frequency = frequency / total x 100%
Cumulative frequency = running total of the frequencies
Cumulative % = cumulative frequency / total x 100%
The last row of the cumulative columns always equals the total count and 100 percent. Percentages are rounded to two decimals for display.
Twelve survey ratings
Twelve people rate a product from 1 to 5: 3, 5, 4, 3, 2, 5, 3, 4, 3, 1, 5, 4. The rating 1 appears once, 2 once, 3 four times, 4 three times and 5 three times. The cumulative counts are 1, 2, 6, 9 and 12, and the relative frequencies are 8.33%, 8.33%, 33.33%, 25% and 25%.
The most frequent rating is 3, with 4 of 12 responses (33.33%). For the simple list 1, 1, 2 the frequencies are 2 and 1. Grouping the values 12, 15, 23, 27, 31, 38 and 44 into classes of width 10 starting at 12 gives counts of 2, 3, 1 and 1.
Counting values and counting classes
A table of each value suits data with a small number of distinct outcomes, such as ratings, dice rolls or categories. When values are continuous, such as heights or prices, almost every value is different, so grouping them into classes shows the shape of the data instead.
Class width and the starting point change how the data look. Try more than one width. Too narrow and every class is nearly empty, too wide and the shape disappears.
Relative and cumulative columns
Relative frequency lets you compare data sets of different sizes. The cumulative columns answer questions such as how many responses were 3 or lower. They are also how percentile ranks are read from a table.
For summary numbers on the same list use the descriptive statistics calculator or the five number summary calculator. To work with the chances of events directly, see the probability calculator.
Assumptions and limits
- Each class includes its lower limit and excludes its upper limit, so a value equal to a class boundary goes in the higher class.
- Words are counted without regard to capital letters, and the first spelling seen is shown.
- Up to 5,000 values and 200 rows are supported. Beyond that the tool asks you to group the data.
- Entries that are not numbers are treated as words when any entry in the list is not a number.
Frequently asked questions
What is a frequency distribution?
It is a table that shows how many times each value, or each range of values, occurs in a data set. It is often extended with relative and cumulative columns.
What is relative frequency?
Relative frequency is a value's count divided by the total number of values, usually shown as a percent. It makes counts comparable between groups of different sizes.
How do I choose a class width?
Pick a width that gives roughly 5 to 15 classes for a typical list, then adjust. Round numbers such as 5, 10 or 100 make the table easier to read, and the first class should start at or below the smallest value.
Can I count words or categories instead of numbers?
Yes. Enter the words separated by commas or new lines and use the Each value option. The table lists the most common word first and counts capital and lowercase spellings together.