Lesson 2 notes

# Lesson 2 notes - The distribution of a variable shows its...

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The distribution of a variable shows its pattern of variation, as given by the values of the variables and their frequencies. The following data set, SAT_DATA.XLS , or SAT_DATA.MTW (data from College Board) contains the mean SAT scores for each of the 50 US states and Washington D.C., as well the participation rates and geographic region of each state. The data patterns however are not yet clear. To get an idea of the pattern of variation of a categorical variable such as region, we can display the information with a bar graph or pie chart . This should result in the following pie chart: In Minitab, if you place your mouse over any slice of the pie you will get the value of the overall percentage of the pie that region covers. For example, place your mouse over the blue colored slice (again this has to be done in Minitab not on the notes!) and you will see that for the Region MA (Mid Atlantic) 5.9% of the 50 states plus Washington D.C. fall into this category. To produce a bar graph or bar chart, return to the menu bar in Minitab and from the Graph options select Bar Chart then Simple. The steps will proceed similar from Step 3 above. In the Minitab Bar Chart, however, placing your mouse over a bar produces the number within that category. For example, if you place your mouse over the region labeled MA (again this has to be done in Minitab not on the notes!) you will see that three (3) of the 50 states plus Washington D.C. are classified as Mid Atlantic. Note that 3/51 equals the 5.9% from the pie chart:

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But what of variables that are quantitative such as math SAT or percentage taking the SAT? For these variables we should use histograms , boxplots , or stem-and-leaf plots . Stem-and-leaf plots are sometimes referred to as stemplots. Histograms differ from bar graphs in that the represent frequencies by area and not height. A good display will help to summarize a distribution by reporting the center , spread , and shape for that variable. For now the goal is to summarize the distribution or pattern of variation of a single quantitative variable. To draw a histogram by hand we would: 1. Divide the range of data (range is from the smallest to largest value within the data for the variable of interest) into classes of equal width. For the math SAT scores the range is
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## This note was uploaded on 05/31/2011 for the course STAT 200 taught by Professor Andyregards during the Spring '11 term at World College.

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Lesson 2 notes - The distribution of a variable shows its...

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