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## 8th grade

### Unit 7: Lesson 4

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
- Analyze two-way frequency tables
- Create two-way relative frequency tables
- Interpreting two-way tables
- Interpret two-way tables

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# Two-way relative frequency tables

AP.STATS:

UNC‑1 (EU)

, UNC‑1.P (LO)

, UNC‑1.P.3 (EK)

CCSS.Math: , Worked example video where we are asked to find a two-way table of column relative frequencies.

## 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.