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Chapter 1

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University of Guelph
Sociology and Anthropology
SOAN 3120
Michelle Dumas

Chapter 1: Picturing Distributions with Graphs Statistics is the science of data Individuals and Variables  Any set of data contains information about some group of individuals are the objects described by a set of data, they may be people but they can be animals or things  The information is organized in variables is any characteristics of an individual, a variable can take different values for different individuals When planning a statistical study ask yourself the questions: 1. Who? What individuals do the data describe? How many individuals appear in the data? 2. What? How many variables do the data contain? What are the exact definitions of these variables? In what unit of measurement is each variable recorded? 3. Where? Student GPAs ad SAT scored will vary from college to college depending on many variables, including admissions “selectivity” for the college 4. When? Students change from year to year, as do prices, salaries etc. 5. Why? What purpose do the data have? Do we hope to answer some specific questions? Do we want answers from just these individuals or for some larger group that these individuals are supposed to represent? Are the individuals and variables suitable for the intended purpose?  Categorical variable places an individual into one of several groups of categories  Quantitative variable takes numerical values for which arithmetic operations such as adding and averaging make sense, the values of a quantitative variable are usually recorded in a unit of measurement such as seconds or kilograms  Most data tables follow this format – each row is an individual, and each column is a variable  Spreadsheets are commonly used to enter and transmit data and do simple calculations Categorical Variables: Pie Charts and Bar Graphs  Statistical tools and ideas help us examine data in order to describe their main features, this is called exploratory data analysis  There are two principles which help us organize exploration of a set data 1. Begin by examining each variable by itself, then move on to study the relationships among the variables 2. Begin with a graph or graphs, then add numerical summaries of specific aspects of the data  The proper choice of graph depends on the nature of the variable  To examine a single variable we usually want to display its distribution o Distribution of a variable tells us what values it takes and how often it takes these values o 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  It’s a good idea to check data for consistency o The percents should add to 100% or in fact 99.9% because of rounding, this is called round off error o Round off error don’t point to mistakes in our work just to the effect of rounding off results  Pie Charts o Show the distribution of a categorical variable as a “pie” whose slices are sized by the counts of percents for the categories o A pie chart must include all the categories that make up a whole o Use a pie chart only when you want to emphasize each category’s relation to the whole  Bar Graphs o Represent each category as a bar o The bar heights show the category counts or the percents o Bar graphs are easier to make then pie charts and also easier to read o It is often best to arrange the bars in order of height that way we can see immediately which majors appear most often o Bar graphs are more flexible than pie charts, both graphs can display distribution of a categorical variable, but a bar graph can also compare any set of quantities that are measured in the same units  Bar graphs and pie charts are mainly tools for presenting data: they help your audience grasp data quickly  Since it is easy to understand data on a single categorical variable without a graph, bar graphs and pie charts are of limited use for data analysis Quantitative Variables: Histograms  Quantitative variables often take on many variables  The distribution tells us what values the variable takes on and how often it takes these values  A graph of the distribution is clearer if nearby values are often grouped together  The most common graph of the distribution of one quantitative variable is a histogram  Although histograms resemble bar graphs, their details and uses are different o A histogram displays the distribution of a quantitative variable  The horizontal axis of a histogram is marked in the units of measurement for the variable o A bar graphs compares the sizes of different quantities o The horizontal axis of a bar graph need not have any measurement
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