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Unformatted text preview: Looking at Data  Distributions Displaying Distributions with Graphs IPS Chapter 1.1 2009 W.H. Freeman and Company Objectives (IPS Chapter 1.1) Displaying distributions with graphs Variables Types of variables Graphs for categorical variables Bar graphs Pie charts Graphs for quantitative variables Histograms Stemplots Stemplots versus histograms Interpreting histograms Time plots Variables In a study, we collect informationdatafrom individuals . Individuals can be people, animals, plants, or any object of interest. A variable is any characteristic of an individual. A variable varies among individuals. Example: age, height, blood pressure, ethnicity, leaf length, first language The distribution of a variable tells us what values the variable takes and how often it takes these values. Two types of variables Variables can be either quantitative Something that takes numerical values for which arithmetic operations, such as adding and averaging, make sense. Example: How tall you are, your age, your blood cholesterol level, the number of credit cards you own. or categorical. Something that falls into one of several categories. What can be counted is the count or proportion of individuals in each category. Example: Your blood type (A, B, AB, O), your hair color, your ethnicity, whether you paid income tax last tax year or not. How do you know if a variable is categorical or quantitative? Ask: What are the n individuals/units in the sample (of size n )? What is being recorded about those n individuals/units? Is that a number ( quantitative) or a statement ( categorical)? Individuals in sample DIAGNOSIS AGE AT DEATH Patient A Heart disease 56 Patient B Stroke 70 Patient C Stroke 75 Patient D Lung cancer 60 Patient E Heart disease 80 Patient F Accident 73 Patient G Diabetes 69 Quantitative Each individual is attributed a numerical value. Categorical Each individual is assigned to one of several categories. Ways to chart categorical data Because the variable is categorical, the data in the graph can be ordered any way we want (alphabetical, by increasing value, by year, by personal preference, etc.) Bar graphs Each category is represented by a bar. Pie charts The slices must represent the parts of one whole. Example: Top 10 causes of death in the United States 2001 Rank Causes of death Counts % of top 10s % of total deaths 1 Heart disease 700,142 37% 29% 2 Cancer 553,768 29% 23% 3 Cerebrovascular 163,538 9% 7% 4 Chronic respiratory 123,013 6% 5% 5 Accidents 101,537 5% 4% 6 Diabetes mellitus 71,372 4% 3% 7 Flu and pneumonia 62,034 3% 3% 8 Alzheimers disease 53,852 3% 2% 9 Kidney disorders 39,480 2% 2% 10 Septicemia 32,238 2% 1% All other causes 629,967 26% For each individual who died in the United States in 2001, we record what was the cause of death. The table above is a summary of that information. Top 10 causes of deaths in the United States 2001...
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 Spring '09
 Statistics

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