Analyzing a cumulative relative frequency graph

nutritionists measured the sugar content in grams for 32 drinks at Starbucks a cumulative relative frequency graph let me underline that a cumulative relative relative frequency graph for the data is shown below so they have different on the horizontal axis different amounts of sugar in grams and then we have the cumulative relative frequency so let's just make sure we understand how to read this this is saying that zero or zero percent of the drinks have a sugar content have no sugar content this right over here this data point this looks like it's at the point 5 grams and then this looks at looks like it's at zero point one this says that zero point one or I guess we'd say 10% of the drinks that that Starbucks offers has 5 grams of sugar or less this data point tells us that a hundred percent of the drinks at Starbucks has 50 grams of sugar or less the cumulative relative frequency that's what we for each of these points we say this this is the frequency that has that much sugar or less and that's why it just keeps on increasing and increasing as we add more sugar we're going to see we're going to see a larger proportion or larger relative frequency has that much sugar or less so let's read the first question an iced coffee has 15 grams of sugar estimate the percentile of this drink to the nearest whole percent so iced coffee has 15 grams of sugar which would be right over here and so let's estimate the percentile so we can see they actually have a data point right over here and we can see that 20 percent or 0.2 20 percent of the drinks that Starbucks offers has 15 grams of sugar or less so the percentile of this drink if I were to estimate it it looks like it's the relative frequency 0.2 has that much sugar or less and so this percentile would be 20 percent once again another way to think about it to read this you could these two percentages you could say that 20% has this much sugar or less 15 grams of sugar or less so an iced coffees in the 20th percentile let's do another question so here we are asked to estimate the median of the distribution of drinks hint think about the 50th percentile so the median if you were to line up all of the drinks you take the middle drink and so you could view that as well what drink is or exactly at the 50th percentile so now let's look at the 50th percentile would be a cumulative relative frequency of 0.5 which be right over here on our vertical axis another way to think about it is 0.5 or 50% of the drinks are going if we go to this point right over here what has a cumulative relative frequency of 0.5 we see that we are right at looks like this is 25 grams so one way to interpret this is 50% of the drinks have less than or have 25 grams of sugar or less so this looks like a pretty good estimate for the median for the middle data point so the median is approximately 25 grams that half of the drinks have 25 grams or less of sugar let's do one more based on the same data set so here were asked what is the best estimate for the interquartile range of the distribution of drinks so the interquartile range we want to figure out well what's sitting at the 25th percentile and we want to think about what's at the 75th percentile and then we want to take the difference that's what the interquartile range is so let's do that so first the 25th percentile we'd want to look at the cumulative relative frequency so 25th this would be 30th so 25th would be right around here and so it looks like the 25th percentile is that looks like about I don't know and we're estimating here so that looks like it's about this would be 15 looks like I would say maybe 18 grams so approximately 18 grams so once again one way to think about it is 25% of the drinks have 18 grams of sugar or less now look at the 75th percentile so this is 70th 75th would be right over there actually I can draw a straighter line to that I have a line tool here so 75th percentile would put me right over there I don't know that looks like I'll go with 39 grams roughly 39 grams and so what's the difference between these two well the difference between these two it looks like it's about 21 grams so our interquartile range that our estimate of our interquartile range looking at the cumulative relative frequency distribution because we're saying hey look it looks like the 25th percentile looks like 25% of the drinks have 18 grams or less 75% of the drinks have 39 grams or less if we take the difference between these two quartiles this is the first the first quartile this is our third quartile we're going to get 21 grams now if we look at this choice the choices right over here 20 grams definitely seems like the best estimate closest to what we were able to estimate based on looking at this cumulative relative frequency graph