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# lec15 - Chapter 15 Descriptive Statistics An overview of...

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Chapter 15 Descriptive Statistics An overview of the field of statistics is shown in Figure 15.1 (also shown below). As you can see, the field of statistics can be divided into descriptive statistics and inferential statistics (and there are further subdivisions under inferential statistics which is the topic of the next chapter). This chapter is about descriptive statistics (i.e., the use of statistics to describe, summarize, and explain or make sense of a given set of data). A data set (i.e., a set of data with the "cases" going down the rows and the "variables" going across the columns) is shown in Table 15.1. Once you put your data set (such as the one in Table 15.1) into a statistical program such as SPSS, you are ready to obtain all the descriptive statistics that you want (i.e., which will help you to make some sense out of your data). Frequency Distributions One useful way to view the data of a variable is to construct a frequency distribution (i.e., an arrangement in which the frequencies, and sometimes percentages, of the occurrence of each unique data value are shown). An example is shown in Table 15.2 in the book and here for your convenience.

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When a variable has a wide range of values, you may prefer using a grouped frequency distribution (i.e., where the data values are grouped into intervals and the frequencies of the intervals are shown). For the above frequency distribution, one possible set of grouped intervals would be 20,000-24,999; 25,000-29,999; 30,000-34,999; 35,000-39,999; 40,000-44,999. Note that the categories developed for a grouped frequency distribution must be mutually exclusive (the property that intervals do not overlap) and exhaustive (the property that a set of intervals or categories covers the complete range of data values). An example of a grouped frequency distribution is shown on pate 437. Graphic Representations of Data Another excellent way to describe your data (especially for visually oriented learners) is to construct graphical representations of the data (i.e., pictorial representations of the data in two-dimensional space). Some common graphical representations are bar graphs, histograms, line graphs, and scatterplots.
Bar Graphs A bar graph uses vertical bars to represent the data. The height of the bars usually represent the frequencies for the categories that sit on the X axis . Note that, by tradition, the X axis is the horizontal axis and the Y axis is the vertical axis. Bar graphs are typically used for categorical variables. Here is a bar graph of one of the categorical variables included in the data set for this chapter (i.e., the data set shown on page 435). Histograms A histogram is a graphic that shows the frequencies and shape that characterize a quantitative variable. In statistics, we often want to see the shape of the distribution of quantitative variables; having your computer program provide you with a histogram is a simple way to do this.

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