pp.20-33 - 20 Constructing Tables and Graphs to Summarize...

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Constructing Tables and Graphs to Summarize Quantitative Data A frequency distribution is a table of data showing the number (frequency) of observations in each of several non-overlapping classes. Notes that this definition is the same one we used for qualitative data. The difference is, when we have quantitative data, we have to decide what the classes will be. In particular, how many classes and how wide should each class be? Example: Data for in-state tuition for 67 public (flagship) universities is presented for the 2005-2006 academic year on the next page. The tuition data, sorted from lowest to highest, is shown below: 3,180 4,416 5,290 6,010 7,140 8,816 3,208 4,464 5,327 6,068 7,284 9,213 3,426 4,497 5,372 6,280 7,318 9,278 3,497 4,613 5,413 6,320 7,376 9,778 3,532 4,628 5,494 6,378 7,415 10,748 3,672 4,699 5,575 6,399 7,434 11,051 3,772 4,829 5,610 6,801 7,821 11,508 4,000 4,864 5,612 6,910 7,912 4,109 5,008 5,613 6,914 7,945 4,164 5,124 5,634 7,062 8,082 4,320 5,221 5,640 7,112 8,235 4,406 5,278 5,812 7,120 8,624 20
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Construct a frequency distribution for the data. If the data is not already sorted, sort the data from low to high. Decide how many classes (intervals of values) that you will use to display the data. Determine boundaries for the classes. How many classes? As a rule of thumb, somewhere between 5 and 20. If you don’t have a lot of data, a small number of classes is appropriate. Larger data sets can have more classes. The goal is to have enough classes to show the variation in the data set, but not so many that you will have empty classes or a lot of classes with a small percentage of the data in them. The tuition data set we’re looking at is small to medium- sized, so let’s use 8 classes. How wide should we make the intervals? Use the following: Largest data value-Smallest data value Appoximate class width Number of classes = For our data, the approximate class width is: (11,508-3,180)/8 = 8,328/8 =1,041. This width is a little awkward for display. So, instead I’ll use a nice round number of 1,000. The problem with this is that I’ll have to increase the number of intervals to 9 to cover the data range. That’s ok. Notice that some trial and error may be involved in determining 21
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how many and the width of the intervals. It is a subjective decision. We still need to determine the values of the class boundaries or limits. Our first interval must have a starting point at or below the smallest value in the data set. Let’s start right at $3,000. So our first interval is going to be $3000<$4000. This can also be expressed as $3000 to $3999 (why are these two expressions equivalent?). The next interval is $4000 to $4999,
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