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 4% 0.04 7 F 10% 0.10 20 D 12% 0.12 24 C 26% 0.26 51 B 48% 0.48 95 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 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 95 51 24 20 7 0 20 40 60 80 100 ABCDF Grade Freq
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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. Patterns in Line Graphs • Look for overall pattern Trend – a long-term upward or downward movement over time • Look for deviations from the overall pattern Spikes and plunges • Look for seasonal variation A change over time that has a regular pattern; pattern repeats itself at known regular intervals of time
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This note was uploaded on 02/14/2011 for the course STAT 110 taught by Professor Johnson during the Fall '07 term at South Carolina.

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

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