Chapter 1: Picturing Distributions with Graphs PDF

CHAPTER 1: Picturing Distributions with Graphs  In Chapter 1 we cover … Individuals and variables Categorical variables: pie charts and bar graphs Quantitative variables: histograms Interpreting histograms Quantitative variables: stemplots Time plots Statistics is the scie...

CHAPTER 1: Picturing Distributions with Graphs  In Chapter 1 we cover … Individuals and variables Categorical variables: pie charts and bar graphs Quantitative variables: histograms Interpreting histograms Quantitative variables: stemplots Time plots Statistics is the science of data. The first step in dealing with data is to organize your thinking about the data: Individual: an object described by a set of data Variable: characteristic of the individual  Types of Variables Categorical variable: places individuals into one of several groups or categories. Quantitative variable: takes numerical values for which arithmetic operations make sense (usually recorded in a unit of measurement).  Exploratory Data Analysis An exploratory data analysis is the process of using statistical tools and ideas to examine data in order to describe their main features. EXPLORING DATA Begin by examining each variable by itself. Then move on to study the relationships among the variables. Begin with a graph or graphs. Then add numerical summaries of specific aspects of the data.  Distribution of a Variable DISTRIBUTION OF A VARIABLE The distribution of a variable tells us what values it takes and how often it takes these values. The values of a categorical variable are labels for the categories. The distribution of a categorical variable lists the categories and gives either the count or the percent of individuals who fall in each category.  Categorical Data The distribution of a categorical variable lists the categories and gives the count or percent of individuals who fall into that category. Pie Charts show the distribution of a categorical variable as a “pie” whose slices are sized by the counts or percents for the categories. Bar Graphs represent each category as a bar whose heights show the category counts or percents.  Pie Charts and Bar Graphs Field of Study Field Percent of students Arts and humanities 10.6 Biological sciences 14.7 Business 14.5 Education 5.2 Engineering 11.2 Health professions 12.8 Note: for bar Math and computer science 3.7 graphs, Physical sciences 2.4 percents Social sciences 10.1 don’t Other majors 14.9 necessarily Total 100.1  Rounding error add to 100.  Quantitative Data The distribution of a quantitative variable tells us what values the variable takes on and how often it takes those values. Histograms show the distribution of a quantitative variable by using bars whose height represents the number of individuals who take on a value within a particular class. Stemplots separate each observation into a stem and a leaf that are then plotted to display the distribution while maintaining the original values of the variable.  Histograms Appropriate for quantitative variables that take many values and/or large datasets. Divide the possible values into classes (equal widths). Count how many observations fall into each interval (may change to percents). Draw picture representing the distribution―bar heights are equivalent to the number (percent) of observations in each interval.  Histograms  Example: Freshman Graduation Rate, or FGR, Data for 2010-2011 FGR Data FGR Count 20 Number of States 55 -