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Learning Objectives

  • Organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line and bar graphs, stem-and-leaf displays, scatter plots, and box-and-whisker plots.

In previous chapters, you learned about discrete and continuous data and were introduced to categorical and numerical forms of displaying data. In this final chapter, you will learn how to display discrete and continuous data in both categorical and numerical displays, but in a way that allows you to compare sets of data.

Remember that discrete data is represented by exact values that result from counting, as in the number of people in the households in your neighborhood. Continuous data is represented by a range of data that results from measuring. For example, taking the average temperatures for each month during a year is an example of continuous data. Also remember from an earlier chapter how you distinguished between these types of data when you graphed them.

The graph above shows discrete data. Remember that you know this because the data points are not joined. The graph below represents the average temperatures during the months in 2009. This data is continuous. You can easily tell this by looking at the graph and seeing the data points connected together.

2 newer terms used are the categorical and numerical data forms. Categorical data forms are just what the term suggests. These are data forms that are in categories and describe characteristics, or qualities, of a category. These data forms are more qualitative data and, therefore, are less numerical than they are descriptive. Graphs such as pie charts and bar graphs show descriptive data, or qualitative data. Below are 2 examples of categorical data represented in these types of graphs:

Numerical data is quantitative data. Numerical data involves measuring or counting a numerical value. Therefore, when you talk about discrete and continuous data, you are talking about numerical data. Line graphs, frequency polygons, histograms, and stem-and-leaf plots all involve numerical data, or quantitative data, as is shown below:

Box-and-whisker plots are also considered numerical displays of data, as they are based on quantitative data (the mean and median), as well as the maximum (upper) and minimum (lower) values found in the data. The figure below is a typical box-and-whisker plot:

You will spend the remainder of the chapter learning about how to compare sets of categorical and numerical data.

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