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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 relative frequency tables

Relative frequencies show how often something happens compared to the total number of times it could happen. In our example, we calculate the relative frequency of accidents for SUVs by dividing the number of SUVs that had accidents by the total number of SUVs. This gives us a percentage or fraction that tells us how common accidents are for that type of vehicle.

## Want to join the conversation?

- what does relative frequency means?(33 votes)
- Relative means in relation to each other. So if I have 1 car crash and three cars that didn't crash, I would have a 1 in 4 chance (1 out of 4 total cars) of crashing and a 3 in 4 chances that I wouldn't crash. Maybe I have 14 crashes out of 100, which if you do the math, simply reduces to mean that 1 out of 7 total vehicles, will, on average, experience some form of an automobile accident (I could have used 25 out of 100 here, or something easier, but I decided to step up the game) . It's comparing the total number of events within a specified column--say only the column on Ford motor vehicles (this is just an example), and comparing the percentages of each event happening. It's just isolating each variable and comparing the part to a whole within the context of one column. Hope that helps.(45 votes)

- At about2:40, I don't understand the whole rounding to the nearest hundredth thing...? And why does he round up to 0.78? I'm so confused!(13 votes)
- I assume you really do not understand rounding? It does not matter if it is to nearest whole number, tenth, hundredth, etc.

The key to rounding as you are learning it in the beginning is to know what place you are rounding to and what the number to the right of that is.

So if it is to the nearest hundredth, underline the number that is two to the right of the decimal. All the numbers to the left of the underlined number stay the same. My underlined number has two choices - either stay the same or move up one. So the one number to the right of our underlined number tells us which one -

If it is less than 5, then we stay the same

If it is 5 or greater, then we move up one.

So with his .776, we underline the second 7 and ask ourselves does it stay a 7 or move to an 8 (since 6 is after this seven, we choose to move up to an 8 and write .78.

The different one is a 9, if we have to round up to a 10, we have to change the number to the left of our number and move it up one.

Hope this helps on rounding(33 votes)

- Why on earth does the quiz question have you fill in all of the relative frequencies when only giving the row and column totals when you never explained how to do it? Thats really really annoying.(17 votes)
- Thank you, I finally found someone who understands the problem here. All the videos are very simple, but they don’t explain the steps, so how are we expected to do the work that follows. The whole idea is to learn, not lose brain capacity for something that makes no sense.(10 votes)

- I'm having trouble understanding this, any advice?(11 votes)
- Take it slow, go over it multiple times, do the questions with him, and if you're really struggling, YouTube is your best asset. Btw, I know this guy is long gone, I'm just answering this for others who might ask.(2 votes)

- OK! Great video, I understood nicely. But I have a question that maybe isn't the subject. Any way: I see why he sum 28 + 97 = 125, and then 28/125. Its shows the percentage of the accidents involving SUV's vehicles last year. ok!

But what means 28/97, how can I think about that? does It make any sense ?(9 votes)- Basically, your dividing by the column total, which is the whole thing as 1. It's only just when you amplify the column total, like 1.25 that easily modifies the total.(2 votes)

- i dont understand this at all he only does one subject and he adds it up by downwords but some of the tests its adding it sideways and i always end up not passing and its my last test on it im just confused(3 votes)
- The reason we add by column is because we are told to fill in the
*column relative*frequencies.

So, we divide each column by the column total.

For example, the relative frequencies for the SUV column will be:`28∕(28 + 97) ≈ 0.22`

`97∕(28 + 97) ≈ 0.78`

`(28 + 97)∕(28 + 97) = 1.00`

This tells us that 22% of the SUVs in this sample were involved in an accident the past year.(8 votes)

- I assume you really do not understand rounding? It does not matter if it is to nearest whole number, tenth, hundredth, etc.

The key to rounding as you are learning it in the beginning is to know what place you are rounding to and what the number to the right of that is.

So if it is to the nearest hundredth, underline the number that is two to the right of the decimal. All the numbers to the left of the underlined number stay the same. My underlined number has two choices - either stay the same or move up one. So the one number to the right of our underlined number tells us which one -

If it is less than 5, then we stay the same

If it is 5 or greater, then we move up one.

So with his .776, we underline the second 7 and ask ourselves does it stay a 7 or move to an 8 (since 6 is after this seven, we choose to move up to an 8 and write .78.

The different one is a 9, if we have to round up to a 10, we have to change the number to the left of our number and move it up one.

Hope this helps on rounding(6 votes) - I'm so confused... I tried the method on my own problem and I got it incorrect? I followed all the steps and I triple-checked!! Is this just me? :((3 votes)
- In the problems on the real exercises,all the data combined does not equal 1. I'm confused.(4 votes)
- Okay so basically, I'm doing the Khan Academy exercises for this and each time I go through it I use this method Sal uses but I seem to only get the 1st and 4th question right. The 2nd and 3rd are always incorrect, am I using the wrong method? Is there a bug in the exercices, please help me out as fast as possible.(4 votes)
- I think it has to do with whether they ask for the
*row*relative frequencies, or the*column*relative frequencies.

For example, let's say we have a table that looks like this:`75 8`

`84 45`

For the row relative frequencies we divide each data point by the sum of the data in that row:`75∕(75 + 8) 8∕(75 + 8)`

`84∕(84 + 45) 45∕(84 + 45)`

Rounding to two decimals, we get`0.90 0.10`

`0.65 0.35`

Notice that each row adds up to 1.00

Similarly, for the column relative frequencies we divide each data point by the sum of the data in that column:`75∕(75 + 84) 8∕(8 + 45)`

`84∕(75 + 84) 45∕(8 + 45)`

Again rounding to two decimals, we get`0.47 0.15`

`0.53 0.85`

Now each column adds up to 1.00(0 votes)

## Video transcript

- [Voiceover] The two-way
frequency table below shows data on type of vehicle driven. So, this is type of vehicle driven, and whether there was an
accident the last year. So, whether there was an
accident in the last year, for customers of All
American Auto Insurance. Complete the following two-way table of column relative frequencies. So that's what they're talking here, this is a two-way table of
column relative frequencies. If necessary, round your answers
to the nearest hundredth. So, let's see what they're saying. They're saying, let's see... Of the accidents within
the last year, 28 were the people were driving an
SUV, a Sport Utility Vehicle and 35 were in a Sports car. Of the No accidents in the
last year, 97 were in SUV and a 104 were in sports cars. Another way you could think of it, of the Sport utility
vehicles that were driven and the total, let's see it's 28 plus 97 which is going to be 125. Of that 125, 28 had an
accident within the last year and 97 did not have an
accident within the last year. Similarly, you could say
of the 139 Sports cars 35 had an accident in the last year, 104 did not have an
accident in the last year. So what they want us to
do is put those relative frequencies in here. So the way we could think about it. One right over here, this represents all the Sport utility vehicles. So one way you could think about, that represents the whole
universe of the Sport Utility Vehicles, at least the
universe that this table shows. So, that's really representative
of the 28 plus the 97. And so, in each of these we want to put the relative frequencies. So this right over here is going to be 28 divided by the total. So over here is 28,
but we want this number to be a fraction of the total. Well the fraction of
the total is gonna be, 28 over 97 plus 28. Which of course is going to be 125. Actually let me just write
them all like that first. This one right over here
is going to be 97 over 125. And of course, when you
add this one and this one, it should add up to one. Likewise, this one's
going to be 35 over 139. 35 plus 104. So, 139. And this is going to be
104 over 104 plus 35. Which is 139. So, let me just calculate
each of them using this calculator. Let me scroll down a little bit. And so, if I do 28 divided by 125, I get 0.224. They said round your answers
to the nearest hundredth. So this is 0.22. No accident within the last
year, 97 divided by 125. So 97 divided by 125 is equal to, see here if I rounded to the nearest hundredth
I'm gonna round up. 0.78, so this is 0.78. Then, 35 divided by 139. 35 divided by 139, is equal to, round to the
nearest hundredth, 0.25. 0.25. And then 104 divided by 139. 104 divided by 139, gets me if I round to the nearest hundredth, 0.75. 0.75, then I can check my answer. And I got it right. But the key thing here is to make sure we understand what's going on here. So, we could- One way to think about this is 22% of the Sport utility vehicles had an
accident within the last year. Or you could say .22 of them. And you could say 78% or 0.78 of the Sport utility vehicles had no accidents. Likewise, you could say
25% of the Sports cars had an accident within the last year. And 75% did not have
an accident last year. So, it allows you think more in terms of the relative frequencies,
the whole, the percentages, however you want to think about it. While this gives you the actual numbers.