Chapter 1 Exploring Data Introduction Data Analysis Making

+ Chapter 1: Exploring Data Introduction Data Analysis: Making Sense of Data The Practice of Statistics, 4 th edition - For AP* STARNES, YATES, MOORE

+ Chapter 1 Exploring Data n Introduction: Data Analysis: Making Sense of Data n 1. 1 Analyzing Categorical Data n 1. 2 Displaying Quantitative Data with Graphs n 1. 3 Describing Quantitative Data with Numbers

+ Introduction Data Analysis: Making Sense of Data Learning Objectives After this section, you should be able to… ü DEFINE “Individuals” and “Variables” ü DISTINGUISH between “Categorical” and “Quantitative” variables ü DEFINE “Distribution” ü DESCRIBE the idea behind “Inference”

n 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 n Statistics

n Letter grade (categorical) from scores on exams (quantitative) n Reporting exceeds the standard, meets standard, or does not meet standard (categorical) based on results of standardized test scores (quantitative) Not every variable that takes number values is quantitative! n Zip code—categorical n Area codes—categorical n Floor of a building that employees work on—categorical Data Analysis n Common to transform from categorical to quantitative. + n

Virginia 4 22 Male California 1 30 Male New York 4 34 Female Age Gender 61 27 27 33 49 26 44 Female Male Female Marital Status Married Married Never married/ single Separated Total Income Travel time to work 21000 21300 30000 26000 15100 25000 43000 20 20 5 10 25 15 10 3000 0 40000 15 30000 40 (a) Who are the individuals in this data set? (b) What variables are measured? Identify each as categorical or quantitative. In what units where the quantitative variables measured? (c) Describe the individual in the first row. Example: U. S. Census Kentucky Florida Wisconsin California Michigan Virginia Pennsylvania Number of Family Members 2 6 2 4 3 3 4 State + Here is information about 10 randomly selected US residents from the 2000 census imported using Fathom software.

Definition: Distribution – tells us what values a variable takes and how often it takes those values Example Variable of Interest: MPG Dotplot of MPG Distribution Data Analysis variable generally takes on many different values. In data analysis, we are interested in how often a variable takes on each value. + n. A

Examine each variable by itself. Then study relationships among the variables. Start with a graph or graphs Add numerical summaries + Data Analysis How to Explore Data

Check your understanding is a car buff who wants to find out more about vehicles that students at his school drive. He gets permission to go to the student parking lot and record some data. Later, he does some research about each model of car on the Internet. Finally, Jake makes a spreadsheet that includes each car’s model, year, color, number of cylinders, gas mileage, weight, and whether it has a navigation system. n Who are the individuals in Jake’s study? n What variables did Jake measure? Identify each as categorical or quantitative. + n Jake

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…

Activity: Hiring Discrimination Follow the directions on Page 5 n Perform 5 repetitions of your simulation. n Turn in your results to your teacher. n Teacher: Right-click (control-click) on the graph to edit the counts. Frequency Class Simulation Data 30 25 20 15 10 5 0 26 14 3 0 3 14 10 2 0 0 1 2 3 4 5 6 7 8 Number of Female Pilots (out of 8) Data Analysis n

+ Introduction Data Analysis: Making Sense of Data Summary In this section, we learned that… ü A dataset contains information on individuals. ü For each individual, data give values for one or more variables. ü Variables can be categorical or quantitative. ü The distribution of a variable describes what values it takes and how often it takes them. ü 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. üBar Graphs üPie Charts üTwo-Way Tables üConditional Distributions We’ll also learn how to organize a statistical problem.

+ Homework Textbook pg 7 Problems: 1, 3, 5, 7, 8