Topic 1.3: Representing a Categorical Variable with Tables
Representing a Categorical Variable with Tables
Video Follow-Along Worksheet
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Learning Objectives:
Represent categorical data using a frequency table.
Represent categorical data using a relative frequency table.
Convert category counts into proportions or percentages.
Describe categorical data using counts and relative frequencies.
Use table values to justify claims about categorical data in context.
Essential Knowledge:
A frequency table gives the number of cases falling into each category.
A relative frequency table gives the proportion or percent of cases falling into each category.
Percentages, relative frequencies, and rates provide the same information as proportions.
Counts and relative frequencies reveal information that can be used to justify claims about the data in context.
Categorical variables are described by comparing categories and how common they are.
A majority means at least 50% of the cases.
Key Vocabulary
Frequency Table
A table that shows the number of cases in each category.
Relative Frequency Table
A table that shows the proportion or percent of cases in each category.
Frequency
The count of individuals in a category.
Relative Frequency
The proportion or percent of individuals in a category.
Case
Another word for an individual in a data set.
Category
A possible value or label for a categorical variable.
Proportion
A part divided by the whole, often written as a decimal or fraction.
Percent
A proportion written out of 100.
Distribution
How the values of a variable are spread across categories.
Majority
More than half, or at least 50%, of the cases.
Video 1: Representing a Categorical Variable with Tables
[0:00 – 8:06]
1.[0:19]
In this video, you learn how to represent categorical data in form.
2.[0:25]
These tabular representations help us the categorical data.
Superpower Survey Scenario[0:37 – 1:05]
An online survey asked students which superpower they would most like to have: invisibility, telepathy, freeze time, super strength, or fly. The video shows raw data from a random sample of 50 high school students.
3.[0:55]
The survey data come from a random sample of high school students.
4.[1:12]
The individuals are the who completed the online survey.
5.[1:18]
The variable in this data set is .
6.[1:25]
Because the values are category names or labels, this variable is .
7.[1:33]
The big question is how to represent the of this categorical variable.
8.[1:43]
A frequency table gives the number of , sometimes called , in each category.
Frequency Table for Superpower Preference[1:50 – 2:12]
Superpower
Frequency
Fly
9
Freeze time
15
Invisibility
7
Super strength
3
Telepathy
16
9.[1:56]
In the superpower table, students chose fly.
10.[2:09]
Only students chose super strength.
11.[2:18]
A new skill in this lesson is constructing or representations of distributions.
12.[2:34]
A relative frequency table gives the or of individuals in each category.
13.[2:52]
To find relative frequencies, divide each count by the number of students, which is .
14.[2:58]
For fly, 9/50 = or .
Relative Frequency Table for Superpower Preference[2:50 – 3:04]
Superpower
Relative Frequency
Percent
Fly
0.18
18%
Freeze time
0.30
30%
Invisibility
0.14
14%
Super strength
0.06
6%
Telepathy
0.32
32%
15.[3:12]
The learning objective is to represent categorical data using or tables.
16.[3:43]
A majority means at least .
17.[4:22]
Exactly of students chose either fly or telepathy.
18.[4:44]
Invisibility is in popularity, so it is not one of the more popular choices.
Monitoring the Future Practice[5:09 – 7:32]
The video then uses a frequency table from the 2018 Monitoring the Future study about the perceived risk of occasionally vaping nicotine. Key values discussed include 782 for slight risk, 501 for no risk, 377 for great risk, and 191 for can't say, drug unfamiliar.
19.[6:19]
The total number of student responses in the vaping table is .
20.[6:32]
The 782 students who answered slight risk make up , which is over .
21.[7:29]
The response can't say, drug unfamiliar represents of students, so it is not over 10%.
22.[7:40]
Categorical data can be represented with a table or a frequency table.
23.[7:52]
Counts and relative frequencies reveal information you can use to claims about the data in context.
Topic 1.3 Takeaways[7:35 – 8:02]
A frequency table gives the number of cases in each category.
A relative frequency table gives the proportion or percent in each category.
Percentages and proportions help compare categories fairly.
Counts and relative frequencies help justify claims about categorical data in context.
24.
Reflection: Using the superpower survey, explain the difference between a frequency table and a relative frequency table.
25.
Reflection: How did the video use table values to decide whether a claim about categorical data was true or not supported? Use one example from the superpower or vaping scenario.
Exit Ticket
A random sample of 40 students was asked which school lunch side they prefer. The frequency table below summarizes the categorical variable preferred lunch side.
Lunch Side
Frequency
Fruit
12
Chips
18
Salad
6
Yogurt
4
(a) Explain what a frequency table records for this categorical variable.
(b) Find the relative frequency or percent for chips and yogurt.
(c) Decide whether the claim "a majority of students prefer chips" is supported by the table.
(d) Use counts or relative frequencies to justify your answer in context.
Class Responses (Esc to close)
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