Compilation of student responses on last Wednesday’s warm up “Statistics is…” The larger the word, the more often it was used in a student’s definition. THIS LESSON’S FOCUS

Unit 2: Exploring Data with Graphs and Numerical Summaries Lesson 2-1 – Types of Data Essential Question(s) How do we differentiate data? Why does the type of data matter? Probability & Stats

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

Learning Objective 1: Variables A variable is any characteristic that is recorded for the subjects in a study Variables change between subjects and samples (variability) Examples: Marital status, Height, Weight, IQ A variable can be classified as either: Categorical Quantitative

So, variable data can be classified as… Categorical Quantitative

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)

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

Learning Objective 2: Main Features of Quantitative and Categorical Variables  For Categorical variables: a key feature is the frequency or percentage of observations in each of the categories Ex: Which airlines have you flown? (we can make a bar graph or pie chart)  For Quantitative variables: key features are the center and spread (variability) Ex: How much did your last airline ticket cost? (we can calculate the average/mean or mode)

Class Practice #1 Identify the variable type as either categorical or quantitative. Number of siblings in a family County of residence Distance (in miles) of commute to school Marital status Your cell phone area code Quantitative Categorical Talk in your group about other examples of variables that seem quantitative but are actually categorical.

So, variable data can be classified as… Categorical Quantitative Discrete Continuous

Learning Objective 3a: Quantitative Discrete Data/Variables 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

Learning Objective 3b: Quantitative Continuous Variable A quantitative variable is continuous if its possible values form an interval Continuous variables have an infinite number of possible values (decimals/fractions) Examples: Height/Weight Age Blood pressure

Learning Objective 3b: More about Intervals To say that values for an interval, is to say there are real numbers existing between any two whole numbers (i.e. decimals. Example: If I count the tires on a car, possible values are… If I measure the tire pressure of a given tire, possible values are… 3 45… 0… 10… 28 30… Nothing in between DISCRETE CONTINUOUS

Class Practice #2 Identify each of the following variables as continuous or discrete Length of time to take a test Number of people waiting in line Number of speeding tickets received last year Your dog’s weight Money in your wallet Continuous Discrete

* - almost always true Categorical Quantitative Discrete Continuous (a word) (a number) (can be counted) (must be measured) Add these general summaries* flow chart if you find helpful…

Learning Objective 4: Frequency, Proportion, and Percentage A frequency is like a total or count; it tells us how often an observation has occurred. The proportion is calculated by taking the frequency of interest and dividing it by the total number of observations. (Proportion = frequency of x / total observations) The percentage is the proportion multiplied by 100. Proportions and percentages are also called relative frequencies. A number A fraction/decimal A percent KEY IDEA 2 2/ %

If 6 students received an “A” out of 39 students, then, 6 is the frequency 6/39 = is the proportion and relative frequency 15.4% is the percentage.154*100=15.4% Learning Objective 4: Frequency, Proportion, and Percentage EXAMPLE

Class Problem #3 A stock broker has been following different stocks over the last several weeks and has recorded whether a stock is up, the same, or down in value. 1. What is the variable of interest 2. What type of variable is it? 3. What is the mode (most common result)? 4. Add proportions to this frequency table

Learning Objective 5: Complete a Frequency Table A frequency table is a listing of possible values for a variable, together with the number of observations and/ or relative frequencies for each value 403/905.20*905