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Two-way relative frequency tables and associations

Two-way relative frequency tables show us percentages rather than counts. They are good for seeing if there is an association between two variables.

Part 1: Making a relative frequency table

A university surveyed its 200 students on their opinions of campus housing.
Convert the two-way frequency table of the data into a two-way table of row relative frequencies.
(If necessary, round your answers to the nearest percent.)
GenderPositive opinionNegative opinionNeutral opinionTOTAL
Male40361490
Female425612110
TOTAL829226200
GenderPositive opinionNegative opinionNeutral opinionTOTAL
Male
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
percent
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
percent
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
percent
100, percent
Female
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
percent
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
percent
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
percent
100, percent

Part 2: Reading a relative frequency table

problem a
What percent of males had a negative opinion of campus housing?
Round your answer to the nearest percent.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
%

problem b
What percent of females had a negative opinion of campus housing?
Round your answer to the nearest percent.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
%

Part 3: Seeing a relationship in a two-way relative frequency table

Based on the relative frequencies from above, which is a valid conclusion about the relationship between gender and opinion in this data?
Choose 1 answer:
Choose 1 answer:

Want to join the conversation?

  • blobby green style avatar for user alanyusanchez
    when we say 'there is no association between gender and opinion' does this mean the percentages should be equal to make the statement true? or are there exceptions like plus/minus a certain variance?
    (0 votes)
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  • sneak peak green style avatar for user Dodge/Ram.Cummins.2ndGen
    I agree with big daddy
    (2 votes)
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  • leafers sapling style avatar for user akhilandy.24
    I don't get how we can conclusively establish an association here, doesn't the fact that there are more female respondents in the sample make the comparison of relative frequencies biased.
    (0 votes)
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    • blobby green style avatar for user Aiena
      Great question Akhil :-)

      Now, if you randomly take 100 of those male and 100 of those female students, 40 of the male students will have a negative opinion and 51 female students will have a negative opinion of campus housing.

      Although we have 90 males and 110 females, percentages can still help us draw conclusions. Pay attention to the word "Association", which means you can relate them/ compare them (after you've converted them in a percentage form).

      I hope this helped.

      Aiena.
      (4 votes)
  • male robot johnny style avatar for user Salah
    I dont understand what to on this page
    (0 votes)
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    • mr pink green style avatar for user David Severin
      You are just converting from raw numbers to percents.
      On the first one, it asks for row relative, so divide 40/90 • 100 (%) and round to 44. Do this for all the top row, and divide by 110 to get bottom row
      Next questions just use the data you found.
      (3 votes)
  • leaf green style avatar for user 91105796
    when we say 'there is no association between gender and opinion' does this mean the percentages should be equal to make the statement true?
    (1 vote)
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  • starky seedling style avatar for user daddy brooks
    this is dumb and should be no longer possible this is the worst part of my dad every day,i always start getting sad when i do map acc and i always want to trow up i want it sent to the grave yard
    Love Brooks
    (1 vote)
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  • blobby green style avatar for user Mathew Sharyn
    So when there is an association based off of the gender and the opinion the reason why females were the answer is because there percentage was higher?
    (1 vote)
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  • purple pi purple style avatar for user louisaandgreta
    “We saw that 40% of males had a negative opinion of housing, while about 51% of females had a negative opinion of housing.”

    Again how can you compare data that’s in a column when this is a row relative frequency table?
    (1 vote)
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  • blobby green style avatar for user nihal.al.dibany
    Frankely I am confused regarding to the relationship in the relative frequency.
    for last question, why we said that there are association although we are dealt with percent?
    (1 vote)
    Default Khan Academy avatar avatar for user
  • duskpin seedling style avatar for user Roslyn Goulding
    If a question were to ask,"what is the probability that a randomly selected person was male and had a non-positive opinion?" How would one answer this
    (1 vote)
    Default Khan Academy avatar avatar for user