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### Course: AP®︎/College Statistics > Unit 1

Lesson 3: Representing two categorical variables- Two-way frequency tables and Venn diagrams
- Read two-way frequency tables
- Create two-way frequency tables
- Two-way relative frequency tables
- Analyze two-way frequency tables
- Interpreting two-way tables
- Interpret two-way tables
- Mosaic plots and segmented bar charts
- Analyzing mosaic plots
- Mosaic plots

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# Interpreting two-way tables

Two-way tables let us sort a group in two ways. For example, we see how men and women voted in the 2012 US presidential election. We can compare the percentages of men and women who voted for each candidate. Two-way tables help us understand how categories relate.

## Want to join the conversation?

- Correct me if I'm wrong, but, if 52% of Men voted for Romney, and 43% of women did, that would make 95% as a total. Whereas, Obama only got 94%. How does that make Obama win?(34 votes)
- I know this comment is five years old, but this table is talking about
*percentages*not the number of people. In this case, it would mean more females voted than males.(22 votes)

- I am having a hard time with interpreting two way tables. In some of the questions there are like 2 or 3 right answers to choose. i don't understand how to single out one of the choices to get the right answer. plz help.(22 votes)
- me too am having the same problem. Sal only discussed a little part of it and he doesn't explain it detailed since he just said
*percent women and*percent men and then says yes to the question(7 votes)

- Yeah this video doesn't prepare you at all for the practice questions. The video features a simple format then the practice segment goes off the rails.(16 votes)
- Does relative frequency have to be a decimal or can it be a fraction? I've seen people do it different ways, but I'm not sure if that is the proper way?(14 votes)
- The practice problems are a lot more harder & difficult to calculate than this.(14 votes)
- Okay but i still don't understand the difference between the column and row relative frequency(12 votes)
- So men and women are columns of the table.

Obama, Romney, Other and Column Total form the rows of the table.

So basically the difference is the orientation(3 votes)

- I've been getting the following feedback a lot during the exercises: "We only know the column relative frequencies, not the row relative frequencies, so we cannot make this claim." Wouldn't that apply to this video as well?(9 votes)
- From1:08to1:30, how and why can Sal say that? Isn't it supposed to be a
**column**relative frequency table.

I don't see how the the question coincides with the table given.

The nuances between a row, column, or table relative frequency whatever are NOT clear.(7 votes) - Was I the only one to notice a video showing"Video games and Violence as the stuck? Watch a video box in the corner lol(6 votes)
- Sal says that if you were to pick a man there is 52% chance they voted for Romney which i think is a mistake because this 52% is only on the population who voted for Romney not the general population who voted for both candidates other wise less than 10% will be left for the actual winner of the election Obama. so kindly correct it or correct me.(4 votes)

## Video transcript

- The two-way table of column
relative frequencies below shows data on gender and voting
preferences during the 2012 United States presidential election. They give us all this data. They give us this, as they
say, the two-way table of column relative frequencies. So for example this column
right over here is Men. The column total is 1.00, or
you could say 100 percent. And we can see that 0.42
of the Men or 42 percent of the Men voted for Obama. We can see 52% of the
Men or 0.52 of the Men voted for Romney. And we can see that the
Other, neither Obama, 6 percent went for
neither Obama nor Romney. And for Women, 52 percent went for Obama, 43 percent went for Romney and 5 percent went for Other. And then these, this 52 plus 43 plus 5 will add up to 100 percent of the women. During the 2012 United
States presidential election, were male voters more
likely to vote for Romney than female voters? So let's see. If we, there are a
couple of ways you could think about it. Well, actually, let's go this way. Male voters, if you were
a man, 52 percent of them voted for Romney. While for the Women, 43 percent
of them voted for Romney. So a man was more likely. If you randomly picked a
man who voted, there was a 52 percent chance they voted for Romney, while if you randomly picked a woman, there was a 43 percent,
of women who voted, there was a 43 percent chance
that she voted for Romney. So yes, male voters
were more likely to vote for Romney than female voters. So the answer is Yes. And we're done.