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# 31 - Chapter 2 Exploring Data with Graphs and Numerical...

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1 Chapter 2: Exploring Data with Graphs and Numerical Summaries Section 2.1: What Are the Types of Data?

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2 Learning Objectives 1. Know the definition of variable 2. Know the definition and key features of a categorical versus a quantitative variable 3. Know the definition of a discrete versus a continuous quantitative variable 4. Know the definition of frequency, proportion (relative frequencies), and percentages 5. Create Frequency Tables
3 Learning Objective 1: Variable A variable is any characteristic that is recorded for the subjects in a study Examples: Marital status, Height, Weight, IQ A variable can be classified as either Categorical, or Quantitative (Discrete, Continuous)

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4 Learning Objective 2: Categorical Variable 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 (Apt, Condo, …) Belief in Life After Death (Yes or No)
5 Learning Objective 2: Quantitative Variable 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

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6 Learning Objective 2: Main Features of Quantitative and Categorical Variables For Quantitative variables: key features are the center and spread (variability) For Categorical variables: a key feature is the percentage of observations in each of the categories
7 Learning Objective 3: Discrete Quantitative Variable 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 Examples: Number of pets in a household Number of children in a family Number of foreign languages spoken by an individual

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8 Learning Objective 3: Continuous Quantitative Variable A quantitative variable is continuous if its possible values form an interval Continuous variables have an infinite number of possible values Examples: Height/Weight Age Blood pressure
9 Class Problem #1 Identify the variable type as either categorical or quantitative 1. Number of siblings in a family 2. County of residence 3. Distance (in miles) of commute to school 4. Marital status

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10 Class Problem #2 Identify each of the following variables as continuous or discrete 1. Length of time to take a test 2. Number of people waiting in line 3. Number of speeding tickets received last year 4. Your dog’s weight
11 Learning Objective 4: Proportion & Percentage (Relative Frequencies) The proportion of the observations that fall in a certain category is the frequency (count ) of observations in that category divided by the total number of observations Frequency of that class Sum of all frequencies The Percentage is the proportion multiplied by 100. Proportions and percentages are also called relative frequencies.

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12 Learning Objective 4:
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