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Interactive Data Analysis Activity: Paper Airplanes and Graph Types

Engage students in a hands-on activity creating and flying paper airplanes to collect data, followed by a lesson on data analysis covering types of variables and graphs. Explore categorical and quantitative data, distribution, frequency tables, marginal and conditional distributions, association, and Simpson’s Paradox. Homework exercises included.

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Interactive Data Analysis Activity: Paper Airplanes and Graph Types

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  1. Warm-Up • List all of the different types of graphs you can remember from previous years:

  2. Paper Airplanes • Make your best paper airplane out of the printer paper provided • Go out in the hall and fly it to your best ability and record how many feet/squares it flies before coming to rest • Do this 3 times • Come back in and record your answer here: • Also put your dot where it needs to go…(dotplot)

  3. Section 1.1 Data Analysis: Categorical and Quantitative Data

  4. Variables… • An Individual is an object described by data from a data set. (Can be people, animals, or objects). • A Variable is any characteristic of an individual. A variable can take different values for different individuals. • A Categorical Variable places an individual into one of several groups or categories. • A Quantitative Variable takes numerical values for which it makes sense to find an average.

  5. Ways to display categorical data • Bar Graphs • Pie Charts • Segmented Bar Graph

  6. To Display Variables • The Distribution of a variable tells us what values the variable takes and how often it takes these values. • A Frequency Table (used for categorical variables) lists individuals by a variable and how many individuals are within the categories of that variable. • A Relative Frequency Table is a frequency table that divides each count by the total, making each value a percentage of the whole.

  7. Roundoff Error • Roundoff Error is when percents or vales are rounded within a relative frequency or frequency table (respectively) which causes the total to not match what is expected. • Ex: Student AP Scores In Millions • Total: 10,531,277 students

  8. Marginal Distribution • A Marginal Distribution is a distribution of one categorical variable in a two-way table. As in, how the variable is distributed among the total of the table. • It is called a marginal distribution because it will literally use the margin of the two-way table.

  9. Conditional Distribution • A Conditional Distribution of a variable describes the values of the variable among individuals who have a specific value of another variable. There is a separate conditional distribution for each value of the other variable.

  10. Example of Conditional Dist. Let’s do the conditional distribution for males… Now females…

  11. Your Answer… • To compare these, we would use a side-by-side bar graph

  12. Association • We say there is an association between two variables if specific values of one variable tend to occur in common with specific values of the other. • For example, if we surveyed all of the fall athletes there would be an association between being male and playing football.

  13. Simpson’s Paradox • Simpson’s Paradox is when an association between two variables that holds for each individual value of a third variable can be reversed when the data for all values of the third variable are combined. • Example: Accident Victims and how they are transported

  14. More information

  15. Homework • Pg. 22 (9-12, 14-15, 17-22, 26)

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