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## Statistics and probability

### Course: Statistics and probability > Unit 1

Lesson 2: Two-way tables- Two-way frequency tables and Venn diagrams
- Two-way frequency tables
- Read two-way frequency tables
- Create two-way frequency tables
- Two-way relative frequency tables
- Create two-way relative frequency tables
- Analyze two-way frequency tables
- Interpreting two-way tables
- Interpret two-way tables
- Categorical data example
- Analyzing trends in categorical data
- Trends in categorical data
- Two-way relative frequency tables and associations
- Two-way tables review

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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.

## Part 2: Reading a relative frequency table

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

## 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?(22 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(4 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 agree with big daddy(3 votes)
- What is the point of this page?(3 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.(1 vote)
- 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.(4 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.(0 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.(4 votes)

- So, my question is, how would we answer questions about a relative frequency table that already has the percentages calculated? For example, what is the probability that a university student has a negative opinion about university housing given that the student is male? If I've already calculated all the percentages, would I just take the probability that is at the intersection of male and negative opinion? Or would that be an "and"/"intersection" answer?(2 votes)
- You would need to divide the probability of the intersection of male and negative opinion, by the probability of male, because of the word "given".

Note that "given" is different from "and".

P(A and B) = P(A intersect B), but P(A given B) = P(A intersect B)/P(B).

Have a blessed, wonderful day!(0 votes)

- 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)
- I don't have many questions but to what extent will their be no relation between the two percents, in this case the genders.(0 votes)
- the blank gender is supreme tell me your thoughts children(3 votes)