Young Countess Dowager 56 Abbey Fri Downton Department Accessory Series and nw07Pnq


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.

56 Dowager and Fri Department Abbey Young Accessory Countess Downton Series

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65 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
Young Countess Dowager 56 Abbey Fri Downton Department Accessory Series and nw07Pnq

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 41-50, 51-60, 61-70, 71-80, 81-90, and 91-100. Here's a finished product :

Class
Frequency
41-50
1
51-60
2
Series Fri Dowager 56 and Countess Department Downton Accessory Abbey Young 61-70
6
71-80
and 56 Downton Fri Dowager Series Abbey Countess Accessory Young Department 8
81-90
14
Series Downton Accessory 56 Young and Fri Countess Department Dowager Abbey 91-100
9

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.

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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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Class
Frequency
Relative Frequency
Percent
Dowager Abbey Countess 56 Young Fri Downton Series Accessory Department and
41-50
1
1/40
2.5%
51-60
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2
2/40
5%
61-70
6
6/40
15%
71-80
8
8/40
Dowager 56 Downton Department and Accessory Countess Abbey Series Young Fri 20%
81-90
14
14/40
35%
Downton Dowager Department and Countess Abbey Series Accessory Young 56 Fri Young Downton Series Dowager Department 56 Fri Accessory Abbey Countess and
91-100
9
9/40
22.5%

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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Class
Frequency
Cumulative (Less Than)
41-50
1
1
56 Series Dowager Fri and Countess Downton Department Accessory Young Abbey
51-60
2
3
61-70
6
9
and Dowager Young Accessory Countess Downton Abbey Series Department Fri 56 71-80
8
17
81-90
14
31
91-100
9
40

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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Class
Frequency
Cumulative (Greater Than)
41-50
1
40
51-60
2
39
56 Young and Department Abbey Accessory Downton Fri Dowager Series Countess
61-70
6
37
71-80
8
31
81-90
14
23
91-100
9
9

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.
Abbey Accessory 56 Young and Downton Countess Dowager Department Series Fri

Practice Questions

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