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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.

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  • aqualine ultimate style avatar for user Haya Aboudan
    what does relative frequency means?
    (31 votes)
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    • female robot grace style avatar for user PeterCullenBurbery
      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.
      (36 votes)
  • aqualine ultimate style avatar for user livy
    At about , 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!
    (11 votes)
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    • mr pink green style avatar for user David Severin
      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
      (26 votes)
  • blobby green style avatar for user 1mackers1
    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.
    (14 votes)
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    • piceratops seedling style avatar for user David994
      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.
      (7 votes)
  • old spice man green style avatar for user Macklin
    I'm having trouble understanding this, any advice?
    (11 votes)
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  • hopper jumping style avatar for user Pedro Ivan Pimenta Fagundes
    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 ?
    (8 votes)
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  • male robot hal style avatar for user jjcross1
    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
    (2 votes)
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    • cacteye blue style avatar for user Jerry Nilsson
      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.
      (7 votes)
  • duskpin seedling style avatar for user rowan
    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)
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  • cacteye blue style avatar for user Laura Fram
    In the problems on the real exercises,all the data combined does not equal 1. I'm confused.
    (4 votes)
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  • mr pants green style avatar for user Christopher B.
    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)
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    • cacteye blue style avatar for user Jerry Nilsson
      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)
  • piceratops ultimate style avatar for user Ben
    why... jusy why this is very confusing
    (3 votes)
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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.