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Comparing distributions with dot plots (example problem)

CCSS.Math: ,

Video transcript

at the Olympic Games many events have several rounds of competition one of these is the men's 100-meter backstroke the upper dot plot shows the times and seconds of the top eight finishers in the semifinal round at the 2012 Olympics in the lower dot the lower dot plot shows the times of the same eight swimmers but in the final round which piece of which pieces of information can be gathered from these dot plots on the semi final round we see that these are the eight times at the eight swimmers we see three swimmers finished it in exactly fifty 3.5 seconds one fin one swimmer finished in fifty three point seven seconds right here and one swimmer right over here finished in fifty two point or fifty two point seven seconds so we can we can think about similar things for each of these dots now in the final round one swimmer here went much much much faster so this is in fifty two point two seconds while this swimmer right over here went slower we don't know which dot he was up here but regardless of which dot he was up here this dot took more time than all of these dots so his time definitely got worse and this is at fifty three point six seven eight seconds fifty three point eight seconds so let's let's look at the the statements and see which of these apply the swimmers had faster times on average in the finals in the finals is this true faster times on average in the finals so if we look at the finals right over here we could take each of these times add them up and then divide by eight the number of times we have let's see if we can get an intuition for where this is because we're really just comparing we're comparing these two these two plots or these two distributions we could say and so let's see if we if we if all the data was these three points and these three points we could kind of find we could Intuit that the the mean would be right around there it would be around fifty three point two or fifty three point three seconds right around there and then we have this point and at this point if you just found the mean of that point at that point so halfway between that point and that point would get you right around there so those two the mean of those two points would bring down the mean a little bit so maybe you know and once again I'm not figuring out the number maybe would be around fifty three point two fifty three point one or fifty three point two seconds so that's my kind of in my intuition for the mean of the final round and now let's think about the mean of the semifinal round so if you just look at if you just look at let's just look at these bottom four five dots if you find the mean you could into it would be maybe right around someplace around here pretty close to around fifty 3.53 point what is that fifty three point three seconds and then you have all these other ones that are at fifty three point five and fifty three point three which will bring the mean even higher so I think it's fair to say that the mean and the final round at the time is less than the mean up here you could calculate it yourself but I'm just trying to look at the distributions and get an intuition here at least in this case it looks pretty clear that the swimmers had a faster times on average in the finals it took them less time one of the swimmers was disqualified from the finals well that's not true we have eight swimmers in the semifinal round and we have eight swimmers in the final round so that one's not true the times and the finals very noticeably more than the times and the semi-finals that does look to be true we see in the semifinals a lot of the times were clumped up right around here at fifty three point three seconds and fifty three point five seconds the high the high time is it as high as this time the low time isn't as low there so the final round is definitely definitely they very noticeably more individually the swimmers all swim faster in the finals that they did in the semi-finals well that's not true well whoever this was they clearly they were one of these data points up here this data point took more time than all of these data points so this represents someone who took more time in the finals than they did in the semi-finals and we got it right