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CCSS.Math: , , , let's say that you have a cherry pie store and you've noticed that there is variability in the number of cherries on each pie that you sell some pies might have over 100 cherries while other pies might have fewer than 50 cherries so what you're curious about is what is the distribution how many of the different types of pies do you have how many pies you have that have a lot of cherries how many pies you have that have very few cherries how many pies are in between and so to do that you set up a histogram what you do is you take each pie in your store let's see if I can draw you draw a pie of some kind it's a cherry pie I don't know if this is an adequate drawing of a pie but you take each of the pies in your in your store and you count the number you count the number of cherries on it so this pie right over here is 1 2 3 4 5 6 7 8 9 10 so you keep counting and let's say it has 32 cherries and you do that for every buy and then you created buckets because you don't want to create just a graph of how many have exactly 32 you just want to get a general sense of things so you create buckets of 30 you say how many pies have between 0 and 29 cherries how many pies have between 30 and 59 including 30 and 59 how many pies have at least 60 and at most 89 cherries how many pies have at least 90 and at most 119 and then how many pies have at least 120 and at most 149 and you know that you don't have any pies that have more than 149 cherries so this should account for everything and then you count them so for example you say ok 5 5 30 to 59 cherries and so we create a histogram or you create a histogram and you make this magenta bar go up to 5 so that's how you would construct this histogram that's what this pie is at different cherry levels histogram is telling us so now that we know how to construct it let's see if we can interpret it based on the information given in the histogram so the first question is based on just this information can you figure out the total number of pies in your store zooming that they're all accounted for by this histogram and I encourage you to pause the video and try to figure it out on your own well what's the total number Five's well let's see there's 5 pies there's five pies that have between that have more than 30 or more and have at least 30 cherries but no more than 59 you have eight pies in this blue bucket you have four pies in this green bucket and then you have what is this five no this is three pies that have at least 120 but no more than 149 cherries and this accounts for all of the pies so the total number of pies you have at the store or five plus eight plus four plus three which is what five plus eight is thirteen plus four seventeen plus three is twenty so there are 20 pies in this store then you can ask more nuanced question what if you wanted to know the number of pies with more than 60 cherries the number of pies with more than 60 so number of pies with I'll say let's say 60 or more 60 or more 60 or more cherries so let's think about it well this magenta bar doesn't apply because these all have less than 60 but all of these other bars are counting pies that have 60 or more cherries this is 60 289 this is 19 119 this is 120 149 so it's going to be these eight cherries that are eight these eight pies that are in this bucket plus these four pies plus these three pies so it is going to be essentially everything but this first bucket everything but all the pies except for these five pies have 60 or more cherries so it should be five less than 20 and so let's see 8 plus 4 is 12 plus 3 is 15 which is five less than 20 so using this histogram we can answer a really interesting we can say well how many more pies do we have that have 60 289 cherries than 120 to 149 cherries well we say well we have eight pies that have 60 8960 289 cherries three that have 120 249 so we have five more pies in the sixty to eighty nine category than we do in the 120 to 149 category so a lot of questions that we can start to answer and hopefully this gives you a sense of how you can interpret histograms