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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
Male$40$$36$$14$$90$
Female$42$$56$$12$$110$
TOTAL$82$$92$$26$$200$
GenderPositive opinionNegative opinionNeutral opinionTOTAL
Male
$\mathrm{%}$
$\mathrm{%}$
$\mathrm{%}$
$100\mathrm{%}$
Female
$\mathrm{%}$
$\mathrm{%}$
$\mathrm{%}$
$100\mathrm{%}$

## 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.
%

problem b
What percent of females had a negative opinion of campus housing?
Round your answer to the nearest percent.
%

## 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:

## 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?
(25 votes)
• 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
(6 votes)
• I dont understand what to on this page
(5 votes)
• What he means is that for the first row, the total 90 people is your 100%. Divide 14 by 90 to find what percent for neutral opinion for males. If it is a long decimal, round it. Then use the table that you completed to answer the questions below.
(11 votes)
• I answered 50.91% and was made wrong but 51% is correct. I am little surprised with that as it was not asked that answer need to in whole numbers.
(3 votes)
• “Round… …to the nearest percent”: This also means “round to the whole percent.”
(15 votes)
• 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.
(2 votes)
• 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.
(12 votes)
• I agree with big daddy
(6 votes)
• im obama and im a good obama
(5 votes)
• The sample size is a bit small imo to conclude that there is an association between campus opinion and gender and the margin between the percentages aren't that large.
(2 votes)
• Hi Zepper,

For us to say the sample size is "small" or "adequate" or "good" etc., we need to know what is is total number of male and female students in the university.

We do not have this information; hence, we cannot say anything about our sample size in the above example.

We'll learn in detail about this in our Statistics class. If you're interested, read the below article-
https://en.m.wikipedia.org/wiki/Sample_size_determination

I hope this helped.

Aiena.
(5 votes)
• Why? Is my question just why
(4 votes)
• What is the point of this page?
(4 votes)
• 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?
(2 votes)