AP Statistics Unit 1 Introducing Statistics

Topic 1.4: Representing a Categorical Variable with Graphs

Representing and Comparing Categorical Data with Graphs
Video Follow-Along Worksheet
↻ Already did this one? It stays open even after it’s checked off — just change any answer and click ✓ Check Answers again (no need to Reset). ✨ Grade with AI only ever raises your grade. Make sure you’re signed in so your changes save.
Learning Objectives: Essential Knowledge:

Key Vocabulary

Bar Chart / Bar GraphA graph that displays category counts or proportions with separate bars.
Relative Frequency Bar ChartA bar chart that shows proportions or percents instead of raw counts.
Pie ChartA circular graph that shows how categories make up the whole.
Legend / KeyA guide that tells which colors or slices match which categories.
Axis LabelThe text naming what an axis represents.
ScaleThe values marked on an axis.
FrequencyThe number of cases in a category.
Relative FrequencyThe proportion or percent of cases in a category.
DistributionHow the values of a variable are spread across categories.
Compare DistributionsLook for similarities and differences across groups for the same variable.

Video 1: Representing a Categorical Variable with Graphs

[0:00 – 8:51]
1. [0:24] In this video, you learn how to represent categorical data .
2. [0:30] These graphical representations help you categorical data.
Superpower Survey Scenario [0:35 – 1:17] The lesson returns to the survey asking students which superpower they would most like to have: invisibility, telepathy, freeze time, super strength, or fly. The data come from a random sample of 50 high school students.
3. [1:06] The individuals in this data set are the who completed the survey.
4. [1:11] The variable of interest is .
5. [1:13] Because the values are labels, this is a variable.
6. [1:43] The graph made from the frequency table is a or of the data.
7. [2:12] We can also make a bar chart to show proportions or percents.
Superpower Data Used in the Graphs [1:43 – 2:17]
SuperpowerFrequencyRelative Frequency
Fly90.18
Freeze time150.30
Invisibility70.14
Super strength30.06
Telepathy160.32
8. [2:39] When making graphs, always label your .
9. [2:44] Put the variable name on the axis and frequency or relative frequency on the axis.
10. [3:10] The vertical axis should start at so the graph is not distorted.
11. [3:28] The bars should be equal in , and it is conventional to leave between them.
Bar Chart Best Practices [2:39 – 3:38]
12. [4:47] In the superpower practice question, the statement that was not supported by the graph was choice .
13. [4:44] Freeze time was chosen by students and fly by , so freeze time was not twice as common.
14. [5:23] The most popular superpower choice was .
15. [6:15] A pie chart should include a or key to connect slices to categories.
Screen Media Practice [6:25 – 8:07] The video uses a 2019 Common Sense Media bar chart for teens' daily screen media use and asks which statement is not supported by the graph.
16. [7:54] In the screen media example, choice C was not supported because the comparison was about times as many, not five.
17. [8:23] Two common graphical displays for categorical data are a chart and a chart.

Video 2: Comparing Multiple Sets of Categorical Data

[0:00 – 8:53]
Comparing Boys and Girls [0:47 – 1:30] A teacher surveyed all of her classes and wants to compare superpower preferences for 80 boys and 125 girls.
18. [1:15] The teacher wants to compare superpower preferences for and students.
19. [2:44] When the groups are different sizes, it is better to compare frequencies than raw counts.
20. [3:45] The supported statement was choice because telepathy was preferred by less than of males and almost of females.
21. [4:00] Relative frequencies make comparisons easier when the groups have different .
Relative Frequency Table for Comparing Superpower Preference [4:18 – 4:48]
SuperpowerMales (80)Females (125)
Fly0.250.32
Freeze time0.350.224
Invisibility0.1880.168
Super strength0.1250.04
Telepathy0.0880.248
22. [5:24] A side-by-side relative frequency bar chart should include a so you know which bars belong to which group.
23. [5:35] The bars can be grouped within each superpower , or they could be grouped within each sex.
Tweens vs. Teens Screen Media Use [6:03 – 8:15] The second practice graph compares average daily screen media use for tweens and teens using a side-by-side relative frequency bar chart.
24. [7:32] In the tweens-versus-teens practice question, the supported statement was choice .
25. [7:35] Both tweens and teens had a proportion of for 2+ to 8 hours of screen media use per day.
Topic 1.4 Takeaways [8:16 – 8:43]
26. Reflection: Using the superpower survey of 50 students, explain how a frequency bar chart and a relative frequency bar chart show the same data in different ways.
27. Reflection: Why are relative frequencies better than raw counts when comparing male and female superpower preferences? Use one example from the lesson.

Exit Ticket

A teacher surveyed two grades about their favorite spirit day theme. The categorical variable is preferred spirit day theme.

Theme9th Grade (30)10th Grade (20)
Pajama Day125
Jersey Day68
Twin Day93
Costume Day34

(a) Explain why a relative frequency bar graph would be more useful than a frequency bar graph for comparing these two grades.

(b) Find the relative frequency or percent for Jersey Day in each grade.

(c) Decide whether the claim "Jersey Day was equally popular in both grades" is supported.

(d) Use counts or relative frequencies to justify your answer in context.

Class Responses (Esc to close)

Click a "Class" button next to a question to see responses.