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## AP®︎/College Statistics

### 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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# Two-way frequency tables and Venn diagrams

Sometimes data belongs to more than one category. For example, candies might have chocolate, coconut, both, or neither. We can use Venn diagrams and two-way tables. Venn diagrams show sets and their overlaps. Two-way tables organize data in rows and columns. Both methods help show relationships between categories.

## Want to join the conversation?

- Are Venn diagrams, by convention, limited to two spheres with intersecting areas?(48 votes)
- In theory, you can represent as many overlapping categories as you like. But after 3 or 4, it becomes a waste of time because the Venn diagram gets confusing. And the whole point of visualizing data is to make it clearer, not more confusing. :-)(87 votes)

- This video didn't help me what so ever(9 votes)
- It just explains the utmost basics of Venn Diagrams and Frequency Tables. If you want more, watch more advanced videos.(18 votes)

- can you do a video about problem solving about Venn diagrams(11 votes)
- why is this important in math(4 votes)
- It is a key fundemental that helps you organise your data visually so that you are able to see the relationships between a set of items. It can also help you identify similarities and differences.(14 votes)

- Are those the only two ways you can do it?(2 votes)
- No, of course but those are the most common ones.(11 votes)

- The two way table seems to be the same way that I learned about Mother/Father to offspring trait in my science class. Am I right?(6 votes)
- Yeah, the two-way tables are used in many different subjects. In my 6th grade social studies, we used two-way tables to describe differences between two groups of people.(3 votes)

- would a punnet square be a type of 2 way frequency table?(7 votes)
- Yes, I even use two-way tables in other classes such as Social Studies to compare and contrast.(3 votes)

- Beijing Academy! assemble!(5 votes)
- What is the pointof portraying data in different ways when one is sufficient.(5 votes)
- if you stab cereal are you a cereal killer 🤔(3 votes)
- While the act of stabbing cereal may sound like a play on words with "serial killer," it is important to remember that words have multiple meanings and interpretations.

In this case, stabbing cereal would simply mean piercing or cutting it with a utensil, which is a common action when eating cereal. Therefore, it would not be accurate to say that someone who stabs cereal is a "cereal killer."

It's important to be mindful of the words we use and their meanings, as they can have different connotations and implications in different contexts.(5 votes)

## Video transcript

- So what I have here
are 12 pieces of candy. The ones that are colored
in brown have chocolate on the outside and the ones that have a C on them means that they have coconut on the inside. So for example, this one
over here in the top left, it's made out of chocolate on the outside, but it doesn't have coconut on the inside. While this one right over
here is chocolate on the outside and it has coconut on the inside. While this one, whoops,
I didn't want to do that, while this one right
over here does not have chocolate on the outside, but it does have coconut on the inside. This one right over here has neither chocolate nor coconut. What I want to think
about is ways to represent this information that we are looking at. One way to do it is using a Venn diagram. So let me draw a Venn diagram. So Venn diagram is one
way to represent it. The way it's typically
done, the convention, is that you would make
a rectangle to represent the universe that you
care about, in this case it would be all the chocolates. All the numbers inside
of this should add up to the number of chocolates I have. So it should add up to 12. So that's our universe right over here. Then I'll draw circles
to represent the sets that I care about. So say for this one I care about the set of the things that have chocolate. So I'll draw that with a circle. You could draw them to scale, but I'm not going to draw them to scale. So that is my chocolate set, chocolate. That is my chocolate set. Then I want to have a coconut set. So coconut. Once again, not drawn to scale. I drew them roughly the same size, but you can see the
chocolate set is bigger than the coconut set in reality. Coconut set. Now we can fill in the different sections. So how many of these things have chocolate but no coconut? Let's see, we have one,
two, three, four, five, six have chocolate but no coconut. Let me do that in a different color because I think the colors are important. So let me do it in green. So one, two, three, four, five, and six. So this section right over here is six. Once again, I'm not
talking about the whole brown thing, I'm talking about just this area that I've shaded in green. Now how many have chocolate and coconut? Chocolate and coconut. Well that's going to be one, two, three. So three of them have
chocolate and coconut. Notice that's this section here that's in the overlap between. Three of them go into both
sets, both categories. These three have coconut
and they have chocolate. How many total have chocolate? Well six plus three, nine. How many total have coconut? Well we're going to have to figure that out in a second. So how many have coconut but no chocolate? Well there's only one with
coconut and no chocolate. So that's that one right over there, and that represents this are that I'm shading in in white. So how many total coconut are there? Well one plus three, or
four, and you see that. One, two, three, four. The last thing we'd want to fill in, because notice, six plus three plus one only adds up to 10. What about the other two? Well the other two are
neither chocolate nor coconut. Actually, let me color this. So that's one, two, these are neither chocolate nor coconut. I could write these two right over here. These are neither chocolate nor coconut. So that's one way to
represent the information of how many chocolates, how many coconuts, and how many chocolate and coconuts, and how many neither. But there's other ways
that we could do it. Another way to do it would
be with a two way table. Two way table. On one axis, say the vertical axis, we could say, let me write this, so has chocolate, I'll
write choc for short, and then I'll write no
chocolate, choc for short. Then over here I could write coconut. I want to do that in white. I got new tools and sometimes the color changing isn't so easy. So this is coconut and then over here I'll write no coconut. Then let me make a little table. Make it clear what I'm doing here. So a line there and a line there and why not add a line over here as well. Then I can just fill in
the different things. This cell, this square,
this is going to represent the number that has coconut and chocolate. Well we are already looked into that, that's one, two, three, that's these three right over here. So that's those three right over there. This one right over
here, it has chocolate, but it doesn't have coconut. Well that's this six right over here. It has chocolate, but
it doesn't have coconut. So let me write this is
that six right over there. Then this box would be it has coconut, but no chocolate. Well how many is that? Well coconut no chocolate
that's that one there. Then this one is going to be no coconut and no chocolate. We know what that's going to be. No coconut and no chocolate
is going to be two. If we wanted to, we could even throw in totals over here. We could write, actually
let me just do that just for fun. I could write total, I could write total, and if I total it
vertically, so three plus one this is four, six plus two is eight. So this four is the total number that have coconut that has chocolate and doesn't have chocolate. That's three plus one. This eight is the total
that does not have coconut. No coconut. So the total of no
coconut, and that of course is going to be the six plus this two. We could total horizontally. Three plus six is nine. One plus two is three. What's this nine? That's the total amount of
chocolate, six plus three. What's this three? This is the total amount no chocolate. That's this one plus two. Anyway, hopefully you
found that interesting. This is just different
ways of representing the same information.