Understanding Frequency & Relative Frequency
Perhaps you have heard of the word “frequency” before, and maybe even “relative frequency. Maybe not. Maybe you’re still wondering why this should be important to you, or how it can be used in real life. Let’s say you have just been given a package of your favorite multicolored candy, Skittles. One way to analyze the Skittles is to determine how many of each color you have. This would be the frequency of each color. You could also determine the relative frequency, or the percentage/likelihood that you will get your favorite Skittle, the green one. Now, that’s math with purpose!
Frequency
The frequency is the number of times an event or a number occurs. The frequency is used when creating a graph of the data set known as a histogram. It is considered “how many” occurrences are within a certain range called the “bin width.”
Relative Frequency
The relative frequency can be written as a ratio, a fraction, a probability, or a percent. It is a part to whole comparison. It is the probability that something is occurring out of the total number of occurrences. It is considered the percentage of occurrences within a certain range. Below is the formula that we use to find the relative frequency of an event.
*Note: The sum of all of the relative frequencies will always equal 1, which represents 100%
*Note: this guide may use symbols you aren’t familiar with. View our complete list of Statistics Symbols here.
Tech Help
In StatCrunch
Step 1: Select Graph-Histogram
Within, you can choose frequency or relative frequency for your histogram
In Excel
Step 1: Use “Data Analysis Add- On”
A frequency table and histogram can be created at the same time.
*Note: it does not calculate the Relative Frequency in this manner. Select Data Tab- Choose Data Analysis- Click Histogram.
Now You Try It! Practice Problem
Example One
A group of thirty students were asked what their favorite class was. The following table contains the result of the study. Find the relative frequency for each of the subjects: Math, Science, English, and History.
| Math | Science | Science | English | History | Science | English | Science | English | Math |
| Science | English | Science | History | Science | Math | History | History | Science | History |
| Science | History | Math | English | Science | English | History | Science | English | Science |
Frequency
Step 1: Find the frequency for each of the subjects
Count how many students liked each subject.
- Students who like Math: 4
- Students who like Science: 12
- Students who like English: 7
- Students who like History: 7
Sample Size
Step 2: Either add these numbers to determine the total sample size or refer back to your problem
Reread the information to see if you were given the sample size
- Our sample size is the 30 because we asked a group of thirty students
Relative Frequency
Step 3: Take each of the answers in step 1 and divide by the answer in step 2 to find the relative frequency of each subject
- Math 4/30 = 0.133
- Science 12/30 = 0.4
- English 7/30 = 0.233
- History 7/30 = 0.233
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