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+ Warm-Up Today Warm-up Objective Pre-test Statistics Chapter 1 Classwork/Homework + Introduction Data Analysis: Making Sense of Data Learning Objectives After this section, you should be able to… DEFINE “Individuals” and “Variables” DISTINGUISH between “Categorical” and “Quantitative” variables DEFINE “Distribution” + Chapter 1 Exploring Data Introduction: Data Analysis: Making Sense of Data 1.1 Analyzing Categorical Data 1.2 Displaying Quantitative Data with Graphs 1.3 Describing Quantitative Data with Numbers Data Analysis is the process of organizing, displaying, summarizing, and asking questions about data. Definitions: Individuals – objects (people, animals, things) described by a set of data Variable - any characteristic of an individual Categorical Variable – places an individual into one of several groups or categories. Quantitative Variable – takes numerical values for which it makes sense to find an average. + is the science of data. Data Analysis Statistics Definition: Distribution – tells us what values a variable takes and how often it takes those values Example 2009 Fuel Economy Guide 2009 Fuel Economy Gui de MODEL MPG MODEL 2009 Fuel Economy Guide MPG <new >MODEL MPG 1 Acura RL 922 Dodge Avenger 16 30 Mercedes-Benz E350 24 2 Audi A6 Q uattro 23 Hyundai Elantra 10 17 33 Mercury M ilan 29 3 Bentley Arnage 14 Jaguar XF 11 18 25 Mi tsubi shi Galant 27 4 BMW 5281 28 Kia Optima 12 19 32 Nissan M axi ma 26 5 Buick Lacrosse 28 Lexus GS 350 13 20 26 Roll s Royce Phantom 18 6 Cadill ac CTS 25 Lincolon MKZ 14 21 28 Saturn Aura 33 7 Chevrol et M al ibu 33 Mazda 6 15 22 29 T oyota Camry 31 8 Chrysl er Sebri ng 30 Mercedes-Benz E350 16 23 24 Volkswagen Passat 29 9 Dodge Avenger 30 Mercury M ilan 17 24 29 Volvo S80 Variable of Interest: MPG 25 <new > Dotplot of MPG Distribution Data Analysis generally takes on many different values. In data analysis, we are interested in how often a variable takes on each value. + A variable 2009 Fuel Economy Guide 2009 Fuel Economy Gui de Examine each variable by itself. Then study relationships among the variables. MODEL MPG MODEL + 2009 Fuel Economy Guide MPG <new MODEL > MPG 1 Acura RL 9 22 Dodge Avenger 1630 Mercedes-Benz E350 24 2 Audi A6 Q uattro 1023 Hyundai Elantra 1733 Mercury M ilan 29 3 Bentley Arnage 1114 Jaguar XF 1825 Mi tsubi shi Galant 27 4 BMW 5281 1228 Kia Optima 1932 Nissan M axi ma 26 5 Buick Lacrosse 1328 Lexus GS 350 2026 Roll s Royce Phantom 18 6 Cadill ac CTS 1425 Lincolon MKZ 2128 Saturn Aura 33 7 Chevrol et M al ibu 1533 Mazda 6 2229 T oyota Camry 31 8 Chrysl er Sebri ng 1630 Mercedes-Benz E350 2324 Volkswagen Passat 29 9 Dodge Avenger 1730 Mercury M ilan 2429 Volvo S80 25 Start with a graph or graphs Add numerical summaries Data Analysis How to Explore Data <new > Population Sample + Data Analysis From Data Analysis to Inference Collect data from a representative Sample... Make an Inference about the Population. Perform Data Analysis, keeping probability in mind… + Guided Exercise 1- Using basic terminology Television station QUE wants to know the proportion of TV owners in Virginia who watch the station’s new program at least once a week. The station asked a group of 1000 TV owners in Virginia if they watch the program at least once a week. a. Identify the individuals of the study and the variable. b. Do the data comprise a sample? If so, what is the underlying population? c. Is the variable categorical or quantitative? d. Identify a quantitative variable that might be of interest? + Introduction Data Analysis: Making Sense of Data Summary In this section, we learned that… A dataset contains information on individuals. For each individual, data give values for one or more variables. Variables can be categorical or quantitative. The distribution of a variable describes what values it takes and how often it takes them. Inference is the process of making a conclusion about a population based on a sample set of data. + Looking Ahead… In the next Section… We’ll learn how to analyze categorical data. Bar Graphs Pie Charts Two-Way Tables Conditional Distributions We’ll also learn how to organize a statistical problem. + Problems Marketing Fast Food: USA Today reported that 44.9% of those surveyed (1261 adults) are in fast-food restaurants from one to three times a week. Identify the variable. Is the variable quantitative or qualitative? What is the implied population? + Problems What is the average miles per gallon (mpg) for all new cars? Using Consumer Reports, a random sample of 35 new cars gave an average of 21.1 mpg. Identify the variable. Is the variable quantitative or qualitative? What is the implied population? + Problems The students at Eastmore College are concerned about the ratio of number of students to number of faculty at their school. Using Barron’s Profiles of American Colleges, they took a random sample of 45 colleges in the nation and obtained the student/faculty ratios at these institutions. From this information, they concluded that their student/faculty ratio is higher than those in most colleges in the nation. Identify the variable. Is the variable quantitative or qualitative? What is the implied population? + Problems The archaeological sire of Tara is more than 4000 years old. Tradition states that Tara was the seat of the high kings of Ireland. Because of its archaeological importance, Tara has received extensive study. Suppose an archaeologist wants to estimate the density of ferromagnetic artifacts in the Tara region. For this purpose, a random sample of 55 plots, each of size 100 square meters, is used. The number of ferromagnetic artifacts for each plot is determined. Identify the variable. Is the variable quantitative or qualitative? What is the implied population?