Chapters 10 11 and 12

Chapters 10 11 and 12 - Chapters 10,11, and 12 (Student)...

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Chapters 10,11, and 12 (Student) 1 Graphs, Good and Bad • Recall the definition of statistics: • Statistics is the science of collecting, classifying , presenting , and interpreting data. Types of Variables • Quantitative variable – takes numerical values for which arithmetic operations make sense. ± Examples: amount of money, number of children, distance • Categorical variable – places an individual into one of several groups or categories ± Examples: gender, race, academic major, zip code Distribution of a Variable • The distribution of a variable tells us what values it takes and how often each value occurs. • How do we describe distributions? ± Tables or graphs ± Numerical summaries • There are several graphical (pictorial) ways to describe/display distributions. The method used is determined by the type of variable (data) and the idea to be presented.
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Chapters 10,11, and 12 (Student) 2 Tables and Graphs for Categorical Data • Frequency (count) – the number of times a value of a variable occurs in the data • Relative Frequency – the proportion (fraction or percent) of all observations that have a given value Example: Table of Exam 1 Grades 7% 0.07 8 F 13% 0.13 15 D 13% 0.13 15 C 35% 0.35 42 B 32% 0.32 37 A Percentage Relative Frequency Frequency Grade Graphs for Categorical Data • Basic graphs for summarizing categorical variables (data) are pie charts and bar graphs. • Pie chart – shows the amount of data that belongs to each category as a proportional part of a circle.
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Chapters 10,11, and 12 (Student) 3 Pie Chart of Exam 1 Grades Exam 1 Grades 32% 35% 13% 13% 7% A B C D F Graphs for Categorical Data • Bar graph – shows the amount of data that belongs to each category as proportionally sized rectangular areas (bars). ± Categories are on horizontal axis ± Frequencies (or relative frequencies) are on vertical axis Bar Graph Exam 1 Grades 0 5 10 15 20 25 30 35 40 45 ABCDF Grade Frequency
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Chapters 10,11, and 12 (Student) 4 Pictograms • Variation of the bar graph • All pictures should have the same width, otherwise the pictures can mislead the reader. • Avoid! Line Graphs • Shows behavior of a quantitative variable over time ± Time marked on horizontal axis ± Frequency (or relative frequency) of variable marked on vertical axis Example: A line graph of the average cost of regular unleaded gasoline each month between January 1990 and December 1999.
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Chapters 10 11 and 12 - Chapters 10,11, and 12 (Student)...

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