Chapter 1 Exploring Data 1.1 Displaying Distributions with Graphs

Unit 1 - Exploritory Data Analysis Chapter 1 - Exploring data Displaying Distributions w/ Graphs Displaying Distributions w/ Number Chapter 2 - The Normal Distribution Chapter 3 - Examining Relationships Chapter 4 - More on Two- Variable Data

Learning Objectives After this section, you should be able to… DEFINE “Individuals” and “Variables” DISTINGUISH between “Categorical” and “Quantitative” variables DEFINE “Distribution”

What is Statistics?  Statistics is the science of data.  Data Analysis is the process of organizing, displaying, summarizing, and asking questions about data in order to describe their main features.

Individuals vs. Variables  Individuals – objects described by a set of data (people, animals, things).  We need to determine what types of individuals the data describes, and how many there are.  Variable - any characteristic of an individual. A variable can take different values for different individuals. (ex: A variable for a group of individuals might be height, which most likely would be different for each individual).  We need to determine how many variables there are, what the exact definitions/ descriptions of those variables are, and in what units each variable is recorded.

What should you ask yourself when you come across new data? 1. What and how many individuals are there? 2. What and how many variables are there? 3. What is the reason the data was gathered and what questions are we trying to answer?

 Identify the W's Ian Walker, a psychologist at the University of Bath, wondered whether drivers treat bicycle riders differently when they wear helmets. He rigged his bicycle with an ultrasonic sensor that could measure how close each car was that passed him. He then rode on alternating days with and without a helmet. Out of 2500 cars passing him, he found that when he wore his helmet, motorists passed 3.35 inches closer to him, on average, than when his head was bear? Who: 2500 motorists What: the distance between the cars and the bicycle riders Why: to determine if wearing a helmet influenced how drivers treated bicycle riders When: Where: How: He rigged his bicycle with an ultrasonic sensor that could measure how close each car was that passed him

Two types of Variables Categorical (Qualitative) Variable – places an individual into one of several groups or categories. ex: red, blonde or brunette hair color ex: wood, aluminum, or vinyl siding Quantitative Variable – takes numerical values for which it makes sense to find an arithmetic operation such as adding or finding the average. ex: height, weight, size (not "small" or "large" but actual calculated measurements.

Determine whether the data are qualitative or quantitative. Explain your reasoning. a) College Major e) heights of hot air balloons b) body temperatures of patients f) eye colors of models c) lengths of songs on MP3 player g) Learning Style d) GPA h) age You Try!

Distribution  the distribution of a varialbe tells us what values the variable take and how often it takes these values ex: This class has _____ students aged 15 ______ students aged 16, students _______ aged 17, and ______ students aged 18. The Distribution of a variable therefore becomes the pattern of variation for that variable, which can be represented visually using graph/tables/ etc.....

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.

Tomorrow...  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.

Example 1 FUEL-EFFICIENT CARS Here is a small part of a data set that describes the fuel economy(in miles per gallon) of 1998 model motor vehicles. (a) What are the individuals in this data set? The individuals are vehicles (or “cars”) (b) For each individual, what variables are given? Which of these variables are categorical and whichare quantitative? The variables are: vehicle type (categorical), transmission type (categorical), number ofcylinders (quantitative), city MPG (quantitative), and highway MPG (quantitative).

Example 2 MEDICAL STUDY VARIABLES Data from a medical study contain values of many variables for each of the people who were the subjects of the study. Which of the following variables are categorical and which are quantitative? (a) Gender (female or male) categorical (b) Age (years) quantitative (c) Race (Asian, black, white, or other) categorical (d) Smoker (yes or no) categorical (e) Systolic blood pressure (millimeters of mercury) quantitative (f) Level of calcium in the blood (micrograms per milliliter) quantitative

Example 3 You want to compare the “size” of several statistics textbooks. Describe at least three possiblenumerical variables that describe the “size” of a book. In what units would you measure each variable? Possible answers (units): Number of pages (pages) Number of chapters (chapters) Number of words (words) Weight or mass (pounds, ounces, kilograms...) Height and/or width and/or thickness (inches, centimeters...) Volume (cubic inches, cubic centimeters...)

Example 4 Popular magazines often rank cities in terms of how desirable it is to live and work in each city. Describe five variables that you would measure for each city if you were designing such a study. Give reasons for your choices. Possible answers include: unemployment rate, average (mean or median) income, quality/availability of public transportation, number of entertainment and cultural events, housing costs, crime statistics, population, population density, number of automobiles, various measures of air quality, commuting times (or other measures of traffic), parking availability, taxes, quality of schools.