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CCSS.Math: , 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 in the last year so whether there was an accident in the last year for customers of all American auto insurance complete the following to a table of column relative frequencies so that's what they're talking to a table of column relative frequencies if necessary we round your answers to the nearest hundred so let's see what they're saying they're saying let's see of the accidents within the last year twenty eight were were the people were driving an SUV a sport utility vehicle and thirty five were in a sports car of the no accidents in the last year ninety seven were an SUV and 104 were a sports car or another way you could think of it of the sport utility vehicles that were driven and the total let's see is it's twenty eight plus 97 which is going to be a hundred and twenty five of that hundred twenty five twenty eight had an accident within the last year and ninety seven did not have an accident last year similarly you could say of the one hundred and thirty nine sports cars thirty-five had an accident last year 104 did not have an accident last year and 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 of the sport utility vehicles so in one way you could think about it that's that represents the whole universe of the sport you've the sport utility vehicles at least that the universe that this table shows so that's really representative of the twenty eight plus 97 and so in each of these we want to put the relative frequency so this right over here is going to be twenty eight twenty eight divided by the total notice over here is twenty eight but we want that we want this number to be the fraction of the total well the fraction of the it's going the the fraction of the total is going to be twenty eight over 97 plus twenty eight 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 in this one it should add up to one likewise this one's going to be 35 / 139 35 + 104 so 139 and this is going to be 104 over 104 + 35 which is 139 and so let me just calculate each of them using this calculator so let me scroll down a little bit and so if I do 28 divided by 125 I get zero point two two four they said round your answers to the nearest hundredth so this is zero point two two no accident within the last year 97 / 125 so 97 / 125 is equal to see here if I round to the nearest hundredth I'm going to round up zero point seven eight so this is zero point seven eight then 35 / 139 35 / 139 is equal to round to the nearest hundredth 0.25 0.25 and then 104 / 139 1:04 / 139 it gets me if I round to the nearest hundred 0.75 0.75 and 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 can one way to think about this is 22% of the sport utility vehicles had an accident within the last year or you could say 20 or you could say 0.2 two of them and you could say 78 percent or zero point seven eight of the sports you of the of the sport utility vehicles had no accidents likewise you could say 25 percent of the sports cars had an accident when the last year and 75 did not have an a seventy-five percent did not have an accident the last year so it allows you to 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