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Frequency Tables

Frequency Tables

Author: Katherine Williams
Description:

Calculate relative frequency from a frequency table.

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Tutorial

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This tutorial covers frequency tables. Frequency tables are a great way of organizing the data that you've collected. Now, the word frequency is the same as the word count. You're just totaling up how many times a particular value is recorded. So if I told you to count a stack of books, you'd tell many how many books were in that stack.

The same thing happens with data. If you needed to count how many times a particular value fell between 60 and 65, you just count how many numbers, how many pieces of data you had that fall in that range. The frequency is the same thing. It's just telling us how many times, how frequently that thing appears.

Once you have these frequencies or counts for your data, you can make a frequency table. And that's the method of organization that I was talking about before. It has two columns, one for the category, whatever it is that you're totaling up, and the other side for the frequency, how many time that thing appeared.

Now, this particular form of organization can be used for both qualitative and quantitative data. It groups the data so once they're in that frequency table, you don't see the individual values or the individual data points anymore. It helps us to condense down very large sets into things that are more useful for us and easier to draw interpretations from. We'll go through an example.

Here is just a group of girls. Now, you can choose anything that you want to measure as your category. So you could say wearing black. So our first category is going to be wearing black. Our second category is not wearing black.

Now, for the frequency part, we're just counting up how many people appear for each category. So for in the first one, wearing black, we have 1, 2, 3, 4, 5, 6. So we have 6 people for that category. So our frequency is 6. For the second category, not wearing black, is the other two, 1, 2. So our frequency there is 2.

Oftentimes, you're going to see a total category at the bottom. So we have a total of 8. All our observations added up together is 8. Now, I picked that category pretty arbitrarily. We could do it again for something different.

This time we could do hair up versus hair down. So for hair up, we have 1, 2, 3, 4, 5 girls, and then 1, 2, 3, for hair down. Now, you could pick more than two categories, you can have three or four or many more.

The important thing is that each person has one place that they belong, and only one place that they belong. Otherwise, you're going to have more people that are counted up than you actually have in your total. And the total is a good way to double check to make sure that you found all of your observations. If I accidentally forgot about this girl in the back and I only had 2 for hair down, I'd noticed that added up to 7, but I should have eight. So double check to make sure that you've counted all of your pieces of data whenever you're making a frequency table, and make sure that every piece of data has one spot that they belong in and only that one spot.

Another form of frequency that's useful is relative frequency. Relative frequency is better with larger data sets because what happens is is you start with taking your normal frequencies, and then you divide by the total number of values. This helps us to draw those comparisons for that larger group of data. We'll go through an example of this as well.

This example, we'll work through relative frequency. We're using a large data set. We're using the population for the Twin Rivers Unified School District. In K-6 in their charter schools, they have 18,096 students. In 7-12, they have 12,617 students. And then for adult school, they have 7,562 students. They give us the total, and that's 38,275 students.

To calculate the relative frequency, we're going to take the frequency and divide by the total. And we're going to repeat this for each category-- the frequency divided by the total, the frequency divided by the total. So I'm going to get out my calculator and do that now.

So for the first one, we're doing 18,096 divided by 38,275, and I get 0.47278 and so forth. I'm going to round. I'm going to round to the thousandths place. You can choose to round to the hundredths or the thousands, really, wherever you want. But I choose the thousandths. So I'm going to do 0.473.

And we're going to repeat for 7-12. Clear out. 12,617 divided by 38,275, and we get 0.3296. Now, this time, when I round it to the thousandths place, it's going to be 0.330. We have our final category for the adults. Same thing for relative frequency. I take the number of adults, 7,562, and divide by the total, 38,275, to get a relative frequency of 0.1975, so 0.198.

Now, the total for relative frequency should be 1. But depending on how we rounded, it might be a little above or a little below. So I'm going to add 0.473 plus 0.330 plus 0.198, and I get 1.001. Even though it's not exactly 1, that's OK. It's just the rounding. Sometimes it'll be a little above or a little below. If you're way off, then that's a good signal that you've made a mistake. But being pretty close to 1 is good enough.

Once we've built our relative frequency tables and our frequency tables, we can use them to do other kinds of graphics and displays. Other tutorials cover this more in-depth. This has been your tutorial on frequencies and relative frequencies.

Terms to Know
Frequency

How often a data value, or range of values, occurs.

Frequency Table

A table showing the values of the data, and their respective frequencies.

Relative Frequency

The percent of the data points that take a particular value. This is obtained by dividing the frequency of each value by the total number of data points.