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Two-way frequency tables

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

Want to join the conversation?

  • blobby green style avatar for user Estefany Vazquez
    the question about help Elena organized in the following two way frequency table? How can you resolve it?
    (23 votes)
    Default Khan Academy avatar avatar for user
    • starky ultimate style avatar for user Nazar Khan
      First, the question tells us that Lena has 10 candies that have caramel AND chocolate so thus the first column and first row's value would be 10. Then we are told that there are 3 candies that do NOT contain chocolate OR caramel. This means that the value at column 2, row 2 would be 3. Then we are told that there are 12 candies that contain chocolate. So adding up both values in row 1 should be equal to 12 (10+X=12) which would give us 2 for Column 2, Row 1. We are also told that she has a total of 18 candies so adding up all values should give us 18 (10+2+3+X=18). Thus the value for Column 1, Row 2 would be 3. The complete answer would be:
      C D
      C 10 2
      D 3 3
      (41 votes)
  • blobby green style avatar for user Marco
    How did Lena get 3 candies under the label of do not contain chocolate and also contains caramel? Please help me, I am having trouble understanding.
    (11 votes)
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    • cacteye blue style avatar for user Jerry Nilsson
      We know that there are 18 candies in total, and 12 of them contain chocolate.
      This means that 18 − 12 = 6 candies do not contain chocolate.

      We also know that 3 candies contain neither chocolate nor caramel, and thereby there are 6 − 3 = 3 candies that don't contain chocolate but do contain caramel.
      (29 votes)
  • primosaur ultimate style avatar for user Sam Hung
    I can do the ones with the numbers in the box but when the question doesn't have a box in it then I struggle with the question, how do you do the last question?
    (9 votes)
    Default Khan Academy avatar avatar for user
    • aqualine ultimate style avatar for user John He
      First this is actually a analytic problem. You need to see the items,then to find the boxes that have the same information,and copy the number down.Sometimes it is hard to distinguish the information,you need to compare the items and the information in the boxes.
      (25 votes)
  • boggle blue style avatar for user s_mehki.renney
    whats the point of this bro
    (16 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Lakin Whited
    Ya, The last one is confusing can someone help please?
    (10 votes)
    Default Khan Academy avatar avatar for user
    • duskpin ultimate style avatar for user CC
      The first helpful clue is the second statement: 10 candies contain both chocolate and caramel. Because it contains both flavors, it should be placed between the 'contain chocolate' row and the 'contain caramel' column.
      The next clue: 3 candies contain neither chocolate nor caramel, has the same pattern. It should go in the 'do not contain caramel' column, and the 'do not contain chocolate' row. The fourth statement states that there are 12 candies in total that contain chocolate, meaning that the sum of the'contain chocolate' row should equal 12. 12-10 = 2, so there must be 2 chocolate candies that don't have caramel.
      Finally, we know that there are a total of 18 candies. 18-(10+2+3) = 3. So, there are 3 candies that contain caramel but do not contain chocolate.
      Hope this helps! :)
      (13 votes)
  • piceratops seedling style avatar for user Isaiah Buckley
    waffles are the answer to all of life's problems
    (12 votes)
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  • duskpin ultimate style avatar for user Elizabeth B
    Is relative frequency supposed to be written as a decimal or fraction?
    (4 votes)
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  • aqualine seed style avatar for user Elizabeth penny
    how did u get two for containing no chocolate nor caramel
    (4 votes)
    Default Khan Academy avatar avatar for user
    • female robot grace style avatar for user loumast17
      It says 3 contain neither

      Since 12 contain chocolate and 10 contain both, that means the remaining 2 ONLY contains chocolate. Since there are 12 total and 10 contain both.

      Thensince there are 18 total and 10 contain both that leaves 8, 2 only contain chocolate which leaves 6 and 3 contain neither that leaves 4 that only contain caramel.

      I hope that makes sense.
      (10 votes)
  • aqualine seed style avatar for user SavannahK
    how do I know that the 12 candies that contain chocolate don't contain caramel
    (7 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user lenorrisrobinson44
    How did you find out there were 10 people that like chocolate but hates caramel
    (6 votes)
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