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# chapter2small - Section 2.2 How Can We Describe Data Using...

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Unformatted text preview: Section 2.2 How Can We Describe Data Using Graphical Summaries? May 11, 2009 1 2 Exploring Data with Graphs and Numerical Summaries 2.1 What Are the Types of Data? Variables may be quantitative (numerical) or categorical (qualitative) . Examples of quantitative variables are: * height, age, weight, income. * height, age, weight, income. Examples of categorical variables are: * political affiliation, health status, gender, race, religion, ethnicity. * political affiliation, health status, gender, race, religion, ethnicity. Two types of quantitative variables are discrete and continuous . 1. Discrete variable takes values which are distinct numbers with gaps. * Examples: # of children, # of plane crashes per year, # of cars on the road, value of a stock (in terms of \$(1/8)), home mortgage interest rate (in terms of (1/8)%). * Examples: # of children, # of plane crashes per year, # of cars on the road, value of a stock (in terms of \$(1/8)), home mortgage interest rate (in terms of (1/8)%). 2. Continuous variable takes any value in an interval. * Examples: age, weight. * Examples: age, weight. 2.2 How Can We Describe Data Using Graphical Summaries? Section 2.2 How Can We Describe Data Using Graphical Summaries? May 11, 2009 2 Graphs for Categorical Variables Bar graphs, Pareto charts, and pie charts graph the relative frequency of categorical data. * Start with categorical data; e.g., Democrat, Republican, Independent. * Start with categorical data; e.g., Democrat, Republican, Independent. relative frequency = frequency in the category total # of observations Example: Poll of 400 students at a university, we have 138 Democrats, 146 Repub- licans, and 116 Independents. Construct the bar graph, Pareto chart, and pie chart. * The Pareto chart is a bar graph with relative frequencies ordered from largest to smallest. * The Pareto chart is a bar graph with relative frequencies ordered from largest to smallest. * responses frequency relative frequency Democrat 138 138/400=0.345=34.5% Republican 146 146/400=0.365=36.5% Independent 116 116/400=0.29=29% total 400 1=100% * responses frequency relative frequency Democrat 138 138/400=0.345=34.5% Republican 146 146/400=0.365=36.5% Independent 116 116/400=0.29=29% total 400 1=100% Section 2.2 How Can We Describe Data Using Graphical Summaries? May 11, 2009 3 Dem. Repub. Indep. BAR GRAPH PERCENT 5 10 15 20 25 30 35 Repub. Dem. Indep. PARETO CHART PERCENT 5 10 15 20 25 30 35 Democrat Republican Independent PIE CHART What is the mode in the above graph? * Republican, since it has the largest relative frequency. * Republican, since it has the largest relative frequency. a50 Section 2.2 How Can We Describe Data Using Graphical Summaries? May 11, 2009 4 Graphs for Quantitative Variables Stem-and-Leaf Plots Example: Data: 43, 38, 25, 41, 13, 24, 30, 10, 17, 5, 46, 33, 5, 29, 58, 10, 34, 57, 62, 95, 26, 21, 6, 46 Ordered data: 5, 5, 6, 10, 10, 13, 17, 21, 24, 25, 26, 29, 30, 33, 34, 38, 41, 43, 46, 46, 57, 58, 62, 95 Each stem represents tens, and each leaf represents ones, in this example.Each stem represents tens, and each leaf represents ones, in this example....
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chapter2small - Section 2.2 How Can We Describe Data Using...

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