Chapter 1: Exploring Data

1.1 Displaying Distributions with Graphs (bar graphs, pie charts) hw: pg 7: 1, 3, 4, 5, 8; pg 22: 11, 14, 15, 17 Target Goal: I can graph categorical data.

Introduction Individuals, Variables, EDA Statistics - science of data Any set of data contains information about some group of individuals The information is organized in variables. Individuals - Objects described by a set of data; may be people, animals, or things. Variables - Characteristics of an individual; can take different values for different individuals.

When exploring data, ask the W’s Who - What individuals do the data describe; how many individuals appear in the data. What - How many variables are there; what are the exact definitions of these variables; in what units is each variable recorded. Why - What is the reason the data were gathered.

Types of Variables Categorical variable – (counts) places an individual into one of several groups or categories. Ex. College major, gender Quantitative variable – (measurements) Takes numerical value for which arithmetic operations such as adding and averaging make sense. Ex. Grade point average, test scores

Ex. 1 Census Bureau Web site (see data on page 7, for exercise 7 & 8) Who? Rows describes one individual subjects. What? Columns contain value of one variable. Why? Evaluate both categorical and quantitative data of people surveyed.

Distribution of a Variable The pattern of variation tells us what values the variables takes and how often it takes these values.

“Think – Show- Tell’ How do we organize data? Exploratory data analysis (EDA): using statistical tools and ideas to: Examine data in order to describe their main features. Begin with graph's. Describe: add numerical summaries.

Entering data on calculator: Inspire: Use Appendix B:A6 Use data from page 46, example 56 STAT:Clrlist L1:ENTER STAT;Edit (enter data) Quit to main screen Store list: L1 DRVTM (Don’t delete. We will use this later!)

Displaying categorical variables: (bar graphs and pie charts) The distribution of a categorical variable lists the categories and gives either the count or the percent of individuals who fall in each category.

Ex. 2 The Most Popular Softdrink Bar graph: quickly compares the heights of bars show the counts. remember: label axis, title graph, scale axis, leave space between bars.

Graphs: Good and Bad This ad for DIRECTV has multiple problems. How many can you point out?

Pie chart - Helps to see what part of the whole each group forms. Remember: must include all categories that make up whole =100%. Pie charts mostly done on computer! Pie chart: Advantages - helps an audience grasp the distribution quickly. Disadvantages - takes time and space, cannot see count of each category.

Ex. 2 Accidental Deaths In 1997 there were 92,353 deaths from accidents in the United States. Among these were 42,340 deaths from motor vehicle accidents, 11,858 from falls, 10,163 from poisoning, 4,051 from drowning, and 3,601 from fires.

92,353 total deaths 42,340 11,858 10,163 4,051 3,601 Cause Percent a. Find the percent of accidental deaths from each of these causes, rounded to the nearest percent. What percent of accidental deaths were due to other causes? (1 min) 92,353 total deaths 42,340 11,858 10,163 4,051 3,601 Cause Percent motor vehicle 46 from falls 13 from poisoning 11 from drowning 4 from fires 4 Other 22

Ex. 2 Accidental Deaths cont. Make a well-labeled bar graph of the distribution of causes of accidental deaths. Be sure to include an “other causes” bar. Hint: x axis – causes, 6 types y axis – percent of accidental deaths (5 min)

Accidental Deaths 50 Percent of accidental deaths 40 30 20 10 Mot. veh Falls Drowning Fires Poison other Cause of accidental deaths

Ex. 2 Accidental Deaths cont. Would it also be correct to use a pie chart to display these data? If not, explain why not. You could because the categories use part of a whole (all accidental deaths).