Chapter1 - Chapter 1: Looking at Data-Distributions Section...

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1 Chapter 1: Looking at Data--Distributions Section 1.1: Introduction, Displaying Distributions with Graphs Section 1.2: Describing Distributions with Numbers Learning goals for this chapter: Identify categorical and quantitative variables. Interpret, create (by hand and with SPSS), and know when to use: bar graphs, pie charts, stemplots (standard, back-to-back, split), histograms, and boxplots (regular, modified, side-by-side). Describe the shape, center, and spread of data distributions. Define, calculate (by hand and with SPSS), and know when to use measures of center (mean vs. median) and spread (range, 5-number summary, IQR, variance, standard deviation). Understand what a resistant measure of center and spread is and when this is important. Use the 1.5IQR rule to look for outliers. Draw a Normal curve in correct proportions and identify the mean/median, standard deviation, middle 68%, middle 95%, and middle 99.7%. Perform calculations with the empirical rule, both backwards and forwards. Understand the need for standardization. Big picture: what do we learn in this chapter? Individuals vs. Variables Categorical vs. Quantitative Variables Graphs: Bar graphs and pie charts (categorical variables) Histograms and stemplots (quantitative variables—good for checking for symmetry and skewness) Boxplots (quantitative variables—graphical display of the 5 # summary, modified boxplots show outliers) Describing distributions Shape (symmetric/skewed, unimodal/bimodal/multimodal) Center (mean or median) Spread (usually standard deviation/variance or IQR from the 5 # summary) Outliers If you have a symmetric distribution with no outliers, use the mean and standard deviation. If you have a skewed distribution and/or you have outliers, use the 5 # summary instead.
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2 2 components in describing data or information: Individuals : objects being described by a set of data (people, households, cars, animals, corn, etc.) Variables : characteristics of individuals (height, yield, length, age, eye color, etc.) Categorical : places an individual into one of several groups (gender, eye color, college major, hometown, etc.) Quantitative : Attaches a numerical value to a variable so that adding or averaging the values makes sense (height, weight, age, income, yield, etc.) Distribution of a variable : describes what values a variables takes and how often it takes those values If you have more than one variable in your problem, you should look at each variable by itself before you look at relationships between the variables. Example: Identify whether the following questions would give you categorical or quantitative data. a) What letter grade did you get in your Calculus class last semester? b) What was your score on the last exam? c) Who will you vote for in the next election? d) How many votes did George W. Bush get? e) How many red M&Ms are in this bag?
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Chapter1 - Chapter 1: Looking at Data-Distributions Section...

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