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A frequency table shows a set of values and assigns a frequency to each of them. In other words, how often does each value occur?
You can use frequency tables to organize quantitative or qualitative data, though they are more commonly used for data with qualitative variables.
Let's take a look at an example. A biology teacher gave a quiz to the 20 students in her class. Each of the students received a score out of 10, and she wants to show them how well they performed overall, as a group.
Here are the steps to build a frequency table…
What does the data show? The teacher can now look at how many students received at or below a particular score. She can do this by comparing the first and third columns (the absolute cumulative frequency and the score). Working backward, 20 students scored a 10 or lower–which makes sense, since this is the highest score they could get.
16 students scored a 9 or lower, 15 scored an 8 or lower, 11 scored a 7 or lower, and so on. Knowing this information can help her to decide whether or not she wants to offer a retake quiz.
Let’s continue working with this data set to see how else the teacher can interpret it.
Relative frequency and cumulative relative frequency
Remember that relative frequency is expressed in percentages. These percentages are useful for showing a frequency’s relationship to the greater whole. For example, what percentage of students received an 8?
0 ÷ 20 = 0 2 ÷ 20 = 0.1 1 ÷ 20 = 0.05
0% of students received a score of 1.
10% received a score of 2.
5% received a score of 3, and so on.
0% received a 1.
0% + 10% = 10%, so 10% of students scored a 2 or lower.
10% + 5% = 15%, so 15% of students received a 3 or lower.
What does the data show? Now the teacher can present the quiz results to her students. She can also decide if they performed well enough on the quiz as a class, or if she should offer a retake.
In conclusion…
Hopefully these steps have clarified how to make your own frequency table. Just remember these four tips:
In the next section of the tutorial, we’ll show you how to present data using different types of graphs.
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