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Chapter 2 Exploring Data with Graphs and Numerical Summaries

Learn about the different types of variables in data analysis, including categorical variables that belong to predefined categories and quantitative variables that represent numerical values. Discover the key features of each type and understand the concepts of discrete and continuous quantitative variables.

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Chapter 2 Exploring Data with Graphs and Numerical Summaries

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  1. Chapter 2Exploring Data with Graphs and Numerical Summaries Section 2.1 Different Types of Data

  2. A variable is any characteristic observed in a study. Examples: Marital status, Height, Weight, IQ A variable can be classified as either Categorical (in Categories), or Quantitative (Numerical) Variable

  3. A variable can be classified as categorical if each observation belongs to one of a set of categories: Examples: Gender (Male or Female) Religious Affiliation (Catholic, Jewish, …) Type of Residence (Apartment, Condo, …) Belief in Life After Death (Yes or No) Categorical Variable

  4. A variable is called quantitative if observations on it take numerical values that represent different magnitudes of the variable. Examples: Age Number of Siblings Annual Income Quantitative Variable

  5. For Quantitative variables: key features are the center and spread (variability) of the data. For Categorical variables: a key feature is the percentage of observations in each of the categories. Main Features of Quantitative and Categorical Variables

  6. A quantitative variable is discrete if its possible values form a set of separate numbers, such as 0,1,2,3,…. Discrete variables have a finite number of possible values. If you COUNT them, it is a discrete quantity “How many ….. ?” usually produces discrete data Discrete Quantitative Variable

  7. A quantitative variable is continuous if its possible values form an interval. Continuous variables have an infinite number of possible values. If you MEASURE it, then it’s a continuous variable “How much …. ?” usually produces continuous data Continuous Quantitative Variable

  8. Ordinal Categorical Variable • Data is words, but there is an ORDER or progression to the choices. • EXAMPLES: • ColdStone: Like it, Love it, Gotta have it • Opinion Survey: Strongly disagree, disagree, neutral, agree, strongly agree

  9. Nominal Categorical Variable • Data is words, with NO obvious or natural ORDER. • Favorite flavor: vanilla, chocolate, pistachio, rocky road • What city were you born in?: Phoenix, Glendale, Tuscaloosa, Atlanta, Boston

  10. The proportion of the observations that fall in a certain class or category is: Frequency of that class Sum of all frequencies The percentage is the proportion multiplied by 100. Proportions and percentages are also called relative frequencies. Proportion & Percentage (Relative Frequencies)

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