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Frequency Tables

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Tutorial

Source: Pool balls and tables created by the author

Frequency tables are tables that show how often data occurs. Frequency is the number of times that particular value occurs in a data set. We'll do several examples to show you. And it's easy to summarize those frequencies in a table.

So for instance, suppose I have the 15 billiard balls from a pool table. One of the variables that I might be interested in about these is color. The one ball is yellow, the two ball is blue, the six ball is green, the nine ball is also yellow. I could take the values that the variable color takes and put them in a table. Frequency is how often these values occur. Two of the balls are yellow, two are blue, two are orange, two are green, et cetera. The only one that only has one is black, the eight ball.

Here's another example. This one deals with quantitative data. Suppose an ice cream taste tester was asked to rate his satisfaction of 20 different ice creams. Here are his satisfaction ratings. Construct a frequency table for the square. Try to scribble this out on a separate sheet of paper, pause the video, and let's see if you can do it. What you should have come up with is this. One ice cream received a score of one. None of them received a score of two. Two of them received a score of three, and so on. This is how often this score was received.

One more example. If the data set is very large, like this one, 333 sixth grade students. Often we don't want to look at the raw data, we'd rather just look directly at the frequency table. This is heights rounded to the nearest inch. This means there are 55 59-inch, 4' 11", students. There are 51 5-foot students, 60 inches.

Oftentimes it's preferable not necessarily to just look at frequency, but to say, OK 11, but what percent of the students is that? We can create a value called relative frequency, created by dividing each value by the total. We can use relative frequency, which is percents, to get a better picture of what portion 11 students really is. It's about 3%. And on and on we go. We can fill out the entire table as relative frequencies as opposed to just regular frequencies.

And so to recap, data sets can be shown in frequency tables whether they're qualitative or quantitative. We did examples of both during this tutorial. Frequency tables are particularly useful with large data sets, where we don't want to see all of the raw data, we'd like to see it categorized. And we can see relative frequency to see what percent of the sample goes in each bucket of our frequency table.

So frequency was the raw count, relative frequency was the percent, and both of those values can go into a frequency table. Good luck and we'll see you next time.