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## Histograms

# Interpreting a histogram

AP.STATS:

UNC‑1 (EU)

, UNC‑1.G (LO)

, UNC‑1.G.1 (EK)

CCSS.Math: , , , ## Video transcript

Let's say 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 different types of pies do you have? how may pies do you have that have a lot of cherries, how many pies that have a few cherries, how many pies are in between? So, to do that, you set up a histogram. what you do is you take each pie in your store, (See I can draw a pie in some kind) it's a cherry pie, I don't know if this is adequate of drawing of a pie. You take each pie in your store, and you count the number of cherries on it. This pie has 1,2,3,4,5 6,7,8,9,10,keep counting Let's say it has 32 cherries. And you are going to do it for every pie. and then you create buckets. Because you don't want to create just a graph I'm not having 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 are between 30 and 59, including 30 and 59? how many pies have at least 60 at most 89 cherries? how many pies have at least 90 at most 119? and then how many pies have at least 120 and at most 149? you know that you don't have any pie that have more than 149 cherries so this should account for everything. Then you count them so for example, 5 pies have more than 30 to 59 cherries and so we create a histogram when you create a histogram, you make this magenta bar go up to 5 so that's how you would construct this histogram that's what the pies at different cherry levels histogram is telling us. so now we have 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? soon be there all accounted for by this histogram and I encourage you to pause this video and try to figure it out on your own What was the total number of pies? Let's see. There's five pies there's five pies that 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 ... three pies that have at least 120 but no more than 149 cherries this accounts for all the pies so the total number of pies you have at the store 5 plus 8 plus 4 plus 3 which is what, 5 plus 8 is 13 plus 4,=17, plus 3 is twenty. So there are 20 pies in this store. Then you can ask more a more nuance question. what if you want to know the number of pies with more than 60 cherries the number of pies with more than 60 number of pies with I'll say this 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 these other bars are accounting pies that have 60 or more cherries this is 60 to 89, this is 90 to 119 this is a 120 to 149 so it's going to be these eight cherries sorry, 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 should be five less than 20 Let's see. 8+4=12,plus 3 is 15 which is five less than 20. So using this histogram we can answer really interest question, which would say how many more pies do we have that have 60-89 cherries than 120 to 149 cherries? We have eight pies at 60-89 60-89 cherries, three that have a 120-149 We have five more pies in the 60 to 89 category that we do in the 120 to 149 categories A lot of questions that we can start to answer hopefully this gives you a sense of how you can interpret histograms.