Lesson 2

Relative Frequency Tables

  • Let’s find relative frequencies of categorical data.

Problem 1

A teacher asks their students whether they studied for a quiz, then scores the quiz. A relative frequency table displays some of the information they collected.

  studied did not study
passed quiz 86% 14%
failed quiz 46% 54%

What does the 86% represent?

Problem 2

The accessory choices of 143 people are recorded in the table. 

  wearing a watch no watch
wearing a belt 62 32
no belt 29 20

Create a relative frequency table that could be used to show the percentages of belt wearers who wear a watch or not, as well as the percentages of people without belts who wear a watch or not.

Problem 3

Scientists give two different treatments to people who have the flu and determine if their health improves. The results for the test are in the two-way table.

  treatment 1 treatment 2
improved health 23 25
no improvement 17 35
  1. What percentage of people receiving treatment 1 had improved health?
  2. What percentage of people receiving treatment 2 had improved health?

Problem 4

A group of people are surveyed about whether they have any brothers or sisters or are an only child, and whether they have any pets.

  have sibling only child
have pets 82 105
no pets 141  

Which value could go in the blank cell so that the percentage of only children that have no pets is 37.5%?









Problem 5

Many adults are selected at random to respond to a survey about their favorite season and whether they have allergies or not. The two-way table summarizes the results from the survey.

  allergies no allergies
winter 43 21
spring 12 13
summer 35 33
fall 33 35
  1. Which season is the least popular in this group?
  2. How many more people have allergies than people without allergies in this group?
  3. How many people were surveyed in this group?
(From Unit 3, Lesson 1.)

Problem 6

A random sample of people are asked about their preferences regarding home decoration and their interest in fashion. Complete the two-way table so it has the characteristics listed.

  • 150 people responded to the survey.
  • 70% of the responders do not pay attention to fashion.
  • 33 of the responders who prefer neutral decorations also do not pay attention to fashion.
  • 20 of the responders who pay attention to fashion also prefer colorful decorations in their homes.
prefer colorful decorations prefer neutral decorations
pay attention to fashion
do not pay attention to fashion


(From Unit 3, Lesson 1.)