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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.
GenderPositive opinionNegative opinionNeutral opinionTOTAL
Male40361490
Female425612110
TOTAL829226200
GenderPositive opinionNegative opinionNeutral opinionTOTAL
Male
percent
percent
percent
100, percent
Female
percent
percent
percent
100, percent

Part 2: Reading a relative frequency table

problem a
What percent of males had a negative opinion of campus housing?
%

problem b
What percent of females had a negative opinion of campus housing?
%

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?

Want to join the conversation?

• 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?
• i think so, because when you say "there is an association between gender and opinion" it means that different genders have different opinions...based on the table, anyway
• I agree with big daddy
• 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.
• 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.
• 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.
• 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)
• 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)
• 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)
• “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)
• 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)
• 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)
• Hi Roslyn,

When you say non-positive opinion, do you mean all people who have a positive AND neutral opinion?
Please clarify, and I'll be happy to help.

Aiena.
(1 vote)