1. Data: Categorical vs. Quantitative Mr. Diaz Math 3

2. Content Standards & Goals  Interpreting Categorical and Quantitative Data Standard: Summarize, represent, and interpret data on a single count or measurement variable. Interpreting Categorical and Quantitative Data Standard  Represent data with plots on the real number line (dot plots, histograms, and box plots).  Student objective: Students will learn the differences between categorical and quantitative data and how this determines the method to represent the data.  In order to reach the goal stated above, we must understand the purpose of learning about these types of data, which are studied in the field of statistics  Video: Why Statistics?Why Statistics?

3. The Importance of Data  Data - acts or information used usually to calculate, analyze, or plan something (Merriam-Webster)Merriam-Webster  Question: What are some reasons that lead us to collect data? (3 min. discussion)  To discover trends (poverty, disease, birth rate, temperature)  To assess popularity (goods, laws, elections)  To make connections between two or more trends (cause & effect, etc.)  Ex: Young Adults Ages 18 To 24 Enrolled In Or Completed CollegeYoung Adults Ages 18 To 24 Enrolled In Or Completed College

4. Categorical Data  Data that can fit into one of several categories  Categories share characteristics that allow them to be grouped to form a data set  Concerned about the amount of each category  Can determine the percentage of a category in relationship to the whole  Categorical data does not have a numerical value  Cannot use arithmetic ( +, -, *, ÷) operations because they will not make sense  Examples: Blood types, gender, marital status

5. Graphing Categorical Data Bar Graph  Shows the numerical values of each category  Widely used to relate groups with different characteristics  Categories may not add up to a whole pie Pie Chart  Shows the amount of each category as a percentage of the total amount  These graphs may include the numerical values of each category  Commonly used to show how a resource/group is being divided

6. Quantitative Data  Data that can be analyzed by applying arithmetic operations  Each data value has a numerical value  We can look for the rate of change, the average, how much that data is spread out, and many more calculations  Review! Mean, median, mode, etc. music videomusic video  Concerned with determining trends  Increases and decreases over time  Effectiveness of treatments (experiments)  Examples: Height, annual income, cost of tuition

7. Graphing Quantitative Data Dot Plot  Organizes data by plotting on an coordinate plane  Can connect data points to make hypotheses about increasing/decreasing and other information Box Plot  Created by finding five number summary and plotting each value in a specific order  Minimum, 1 st quartile, median, 3 rd quartile, and maximum Histogram  This graph is divided into several intervals  data values fall within a range CAUTION! This is not a bar plot because a bar plot uses categories. You cannot have a range when using categories.

8. Q: What are the advantages/disadvantages from representing a scenario as categorical or quantitative?  Ex: A class has 30 students. The following information shows the grade breakdown: A – 5, B – 6, C – 8, D – 6, and F – 5  Categorical: We can create a pie chart or bar graph to show the percentage of students with a certain grade  Quantitative: We can find the average grade and the spread of the data from this average  With the given information, answer the question above by spending 3 minutes discussing with your partner.

9. Categorical or Quantitative? Directions: Take 5 minutes to discuss whether the following are examples of categorical or quantitative data sets.  The number of siblings a student in this class has  The distance each student travels to get to school  The amount of hours each student dedicates to studying

10. How to Find Existing Sets of Data  The Internet provides many valuable resources that have an enormous amount of collected data, such as:  Kids Count Data Center Kids Count Data Center  California Department of Education California Department of Education  US Census Bureau US Census Bureau  Q: With so many resources out there, how can we determine if a data set is appropriate for our needs? (3 min Discussion with partner)  May consider the categories values are grouped into  Data is up to date  Can explain how a data set relates to your argument

11. Using Mathematical Software (RStudio)  Easily perform arithmetic calculations  Import data into the program  Use Excel files to transfer data  Graph data using several different methods (pie chart, bar graph, histogram, etc.)  Ex: Young Adults Ages 18 To 24 Enrolled In Or Completed College (slide 3)

12. Assessment Directions: Please use the remaining time in class to write a 3-4 sentence response. These assignments will be completed individually and will not be based on the examples stated in class. Include:  One example each of categorical and quantitative data  The type of graph to represent the data set

13. References  Moore, David, George McCabe, and Bruce Craig. Introduction to the Practice of Statistics. Eighth ed. New York City: W.H. Freeman, 2015.