A frequency distribution is a tool for organizing data. We use it to group data into categories and show the number of observations in each category. Here are some test scores from a math class.
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Lock Key Accessories Assembly Bagger and Werx Saddlebag 370960 xwzIqIYO65  91  85  Countess Abbey Young Series Department Accessory and 56 Fri Downton Dowager 76  85  87  79  93 
82  75  100  70  88  78  83  59 
87  69  89  54  74  89  83  80 
94  67  77  92  82  70  94  84 
96  98  46  70  90  96  88  72 
It's hard to get a feel for this data in this format because it is unorganized. To construct a frequency distribution, you should first identify the lowest and highest values in the list. We do this because we want to be sure that each value in the list fits into one of our categories. The low value here is 46, and the high is 100. A set of categories that would work here is 4150, 5160, 6170, 7180, 8190, and 91100. Here's a finished product :




















We can now see that the biggest number of tests were between 81 and 90, and most of the tests were between 71 and 100.
The low number in each category (or class) is called the lower class limit, and the high number is called the upper class limit.
Now for some guidelines for constructing a frequency distribution.
After the first two rules above, the rest are merely suggestions. Each set of data may require you to violate some of these suggestions. The best advice is to try and follow them whenever possible.
One further extension to the frequency distribution is to look at the percentage of values that show up in each category. This is called a relative frequency distribution or percent frequency distribution. Here's how the above data would be presented in this way.




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The final frequency distribution that we will discuss is the cumulative frequency distribution. Think about the word cumulative, it generally refers to some sort of total. A cumulative frequency distribution is a way to list how many values fit into the first class, the first 2 classes, the first 3 classes, etc., or the last class, the last 2 classes, etc. Here's a cumulative less than frequency distribution for the above set of data.
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The 1 means that there is 1 value that is 50 or less, the 3 means that there are 3 values that are 60 or less, the 9 means that there are 9 values that are 70 or less, and so on.
Now for a cumulative greater than frequency distribution.
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The 40 means that there are 40 values that are 41 or more, the 39 means that there are 39 values that are 51 or more, the 37 means that there are 37 values that are 61 or more, and so on.
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Practice Questions
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