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 Statistics is the science of data. Data Analysis is the process of organizing, displaying, summarizing, and asking questions about data. Data Analysis 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.

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

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

Data Analysis From Data Analysis to Inference Population Sample 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. Identify the individuals of the study and the variable. Do the data comprise a sample? If so, what is the underlying population? Is the variable categorical or quantitative? 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?