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Unformatted text preview: CHAPTER 1 (Section 1.1 and 1.2) In this chapter we will look at how to explore data using some basic techniques. Exploring the Data: (Data Description) We will look at describing data on a single variable by 1. graphing it. 2. finding numerical summaries. Some Vocabulary: Individuals (units): Objects described by a set of data (animals, cars, plots of ground, farms etc). Variables: Characteristic of individuals (weight, color, yield etc). There are two types of variables: Quantitative variable: takes numerical values for which arithmetic operations such as adding and averaging values make sense. (height, weight, age, income, yield, etc.) Categorical variable: places an individual into one of several groups or categories, uses the count or percent of the individuals for each category. (gender, eye color, college major, hometown, etc.) Distribution of a variable: Describes what values a variable takes and how often it takes those values. Example 1 : Identify the unit in the following questions and whether the answer would give you categorical or quantitative data. If it is categorical, state the possible answers. a) What letter grade did you get in your most recent math class? b) What was your score on the last exam? c) What is your GPA? d) What color is this M&M? STAT 301 Spring 2012 Chap 1, Page 1 Graphing Methods: Before we look at graphical methods, we need to look at the two types of variables since each one requires different graphing techniques. Categorical Variable: Places an individual into one of several groups or categories. Examples: Bar graph Pie graph Quantitative Variable: Takes numerical values for which arithmetic operations such as adding and averaging make sense. Examples: Stemandleafplots Histograms Boxplots (discussed later) Categorical variables: (bar graphs and pie charts) Note: Typically with bar graphs, the yaxis represents the frequency (number of observations) in the categories. Example 2 : Messy room example: In a poll of 200 parents of children ages 6 to 12, respondents were asked to name the most disgusting things ever found in their childrens rooms. The results are below (J&C 2005) Most disgusting thing # of parents % of parents Foodrelated 106 53% Animal and insectrelated nuisances 22 11% Clothing (dirty socks and underwear especially) 22 11% Other 50 25% 2 Quantitative Variables: (Stemandleafplots & Histograms) Stemand leafplots: Display the actual values of all observations, good for small amount of data with a value greater than 0. Steps: 1. Order the data. 2. Separate each observation into a stem and leaf (Note: Leaf = final digit) 3. Write stem in a vertical column with the smallest at the top, and draw a vertical line. There is an option of expanding the number of stems by splitting each stem into two (this spreads the distribution)....
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 Spring '08
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