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Course: Statistics and probability > Unit 1

Lesson 2: Two-way tables
Math
Statistics and probability
Analyzing categorical data
Two-way tables
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Two-way frequency tables

Google Classroom
Learn how to read and use two-way frequency tables.
Let's jump right in and look at a two-way frequency table that came from asking 100 students whether they prefer cats or dogs.
PreferenceMaleFemale
Prefers dogs3622
Prefers cats826
No preference26
The columns of the table tell us whether the student is a male or a female. The rows of the table tell us whether the student prefers dogs, cats, or doesn't have a preference.
Notice that there are two variables-- gender and preference-- this is where the two in two-way frequency table comes from.
The cells tell us the number (or frequency) of students. For example, the 36 is in the male column and the prefers dogs row. This tells us that there are 36 male students who prefer dogs.
How many female students prefer cats?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Row and column totals

To find the number of students that prefer cats, we just add up the number of students in the prefers cats row:
PreferenceMaleFemale
Prefers dogs3622
Prefers cats826
No preference26
Students who prefer cats=8+26=34
How many of the students are male?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Let's practice!

Problem 1

Researchers once surveyed college students on their Facebook use. The following two-way table displays data for the sample of students who responded to the survey.
How many students in the survey were in the age category of 18 to 22?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
students
AgeUses FacebookDoes not use Facebook
18 to 22784
23+7067

Problem 2

Researchers once surveyed students on which superpower they would most like to have. The following two-way table displays data for the sample of students who responded to the survey.
How many males in the survey chose to fly as their superpower?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
students
SuperpowerMaleFemale
Fly2612
Invisibility1432
Other108

Problem 3

Researchers surveyed recent graduates of two different universities about their income. The following two-way table displays data for the sample of graduates who responded to the survey.
How many graduates in the sample came from University A?
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
graduates
IncomeUniversity AUniversity B
Under $20,0003540
$20,000 to $39,9999063
$40,000 and over3537

Challenge problem

Lena knows the following information about her box of 18 candies:
  • 10 candies contain both chocolate and caramel.
  • 3 candies contain neither chocolate nor caramel.
  • 12 candies in total contain chocolate.
Help Lena organize the results in the following two-way frequency table.
Contain caramelDo not contain caramel
Contain chocolate
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
Do not contain chocolate
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

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