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Unformatted text preview: 3 3 Chapter 2 Exploring Data with Graphs and Numerical Summaries 2.1 What Are the Types of Data? Categorical Variables – place each observation into groups and they are usually summarized by the percentage of observations in each group. Quantitative Variables – • Discrete – take on a finite number of possible values, such as a count (0, 1, 2, 3, etc.) • Continuous – take on values in an interval, even though sometimes we are limited in our ability to measure them Example: The class list below has all the information for each student in a class at the end of the semester, including their year in school, major, exam grades, project grades, number of absences, their average in the class and their final letter grade in the class. Student ID# Name Yr Major Ex1 Ex2 Pr1 Pr2 Abs Avg Grade 46895382 Aiken, John 1 Psych 78 82 20 24 2 81.6 B 21657845 Bailey, Kim 2 PolSci 62 74 15 19 10 68.0 D 13695544 Carr, May 2 BusAdm 95 92 25 24 0 94.4 A …etc. Which of the previous variables are: Categorical Discrete Quantitative Continuous Quantitative 4 4 2.2 How Can We Describe Data Using Graphical Summaries? The type of graph used depends on the type of variable. Most graphs are done with a computer, particularly for large data sets. Graphs for Categorical Variables: Bar Charts and Pie Charts Example: Year in school for students in classroom Frequency (Count) Proportion Percentage Freshman Sophomore Junior Senior Total Bar Chart Pie Chart 5 5 Histograms are graphs that display quantitative data. We can describe the center, spread, shape, and outliers for a histogram. (We will talk about shape later.) • Center of a Histogram is the balancing point of the graph. • Spread of a Histogram is the range of the values in the graph. • Outliers are points that are separated from the rest of the data. When we are doing this by eye, an outlier will be any point that is more than ½ of the range away from the rest of the data. Example: C3 Frequency 100 90 80 70 60 50 40 50 40 30 20 10 Grades on Exam 1 in Sta 3024 Describe the center, spread and outliers for the above distribution. 6 6 Graphs for Quantitative Variables: Dotplots, StemandLeaf Plots, and Histograms Example: Grades on an exam for a small class: 82, 76, 65, 94, 72, 80, 91, 45, 72, 86, 89 Dotplot Stemplot Histogram For this data set, what can you say about: a) the center of the distribution? b) the spread of the distribution? c) the shape of the distribution? d) unusual observations? 7 7 Some common shapes : Mound or Bellshape Uniform or Rectangular Bimodal Skewed Left Skewed Right 8 8 Examples: For the following graphs, describe their distributions in terms of shape, center, and spread. 1. What age group has the most dangerous drivers? The following graph represents the number of driver deaths (per 100,000 licensed drivers) by age group, for the year 2002....
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This note was uploaded on 12/15/2011 for the course STA 3024 taught by Professor Ta during the Spring '08 term at University of Florida.
 Spring '08
 TA
 Statistics

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