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In this lesson, students study categorical data displayed in two-way tables, bar graphs, and segmented bar graphs. A two-way table is a way to organize categorical data in a table based on 2 variables. A segmented bar graph is a way to visualize the percentage of data within categories. The different graphical representations help students visualize the frequencies and relative frequencies. Relative frequencies are percentages or fractions of the whole represented by a category. While the concepts and structures in this lesson are not very complex, there are many new terms and representations, and students are given the opportunity to study them carefully so that they can make sense of them (MP1).
Let’s look for associations in data.
Print and cut up cards from the Matching Representations blackline master. Prepare 1 set of cards for every 2 students.
A segmented bar graph shows categories within a data set. Each whole bar represents all the data in one main category. Each bar is separated into parts (segments) that show subcategories.
This segmented bar graph shows the percentage of people in different age groups that do and do not have a cell phone. For example, among people ages 10 to 12, about 40% have a cell phone and 60% do not.
A two-way table shows data for 2 categorical variables. One variable is shown in rows and the other in columns. Each entry is the frequency or relative frequency of the category shown by the column and row headings.
This two-way table shows the results of a study. The study looked at how meditation affects the way athletes feel.
| meditated | did not meditate | total | |
|---|---|---|---|
| calm | 45 | 8 | 53 |
| agitated | 23 | 21 | 44 |
| total | 68 | 29 | 97 |