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# Interpreting box plots

AP.STATS:
UNC‑1 (EU)
,
UNC‑1.L (LO)
,
UNC‑1.L.1 (EK)
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UNC‑1.L.2 (EK)
CCSS.Math:

## Video transcript

so I have a box and whiskers plot showing us the ages of students at a party and what I'm hoping to do in this video is get a little bit of practice interpreting this and what I have here are five different statements and I want you to look at these statements pause the video look at these statements and think about which of these based on the information in the box and whiskers plot which of these are for short true which is these are for sure' false and which of these we don't have enough information it could go either way all right so let's let's work through these so the first statement is that all of the students are less than 17 years old well we see right over here that the maximum age that's the right end of this right or whisker is 16 so it is the case that all of the students are less than 17 years old so this is definitely going to be true the next statement at least 75% of the students are 10 years old or older so when you look at this this feels right because 10 is 10 is the value that is at the beginning of the second quartile this is the second quartile right over there and actually let me do this let me do this in a different color so this is the second quartile so 25% of the value of the numbers are in the second or roughly its note sometimes it's not exactly so approximately I'll say roughly 25% are going to be in this second quartile approximately 25% are going to be in the third quartile and approximately 25% are going to be in the fourth quartile so it seems reasonable for saying 10 years old or older that this is going to be this is going to be true in fact you could even have a couple of values in the first quartile that are 10 but to make that a little bit more tangible let's look at some so I'm feeling I'm feeling good that this is true but let's let's look at a little few more examples to make this a little bit more concrete so they don't know we don't know based on the information here exactly how many students are at the party we'll have to construct some scenarios so we could do a scenario let's see if we can do we could do a scenario where well let's see let's see if I can I can construct something where let's see the median is 13 we know that for sure the median is 13 so if I have an odd number I would have 13 in the middle just like that and maybe I have 3 on side and I'm just making that number up I'm just trying to see what I can learn about different types of datasets that would could be described by this box and whiskers plot so 10 is going to be the middle of the bottom half so that's 10 right over there and 15 is going to be the middle of the top half that's what this box and whisker plot is telling us and they of course tell us what the minimum the minimum is 7 and they tell us that the maximum is 16 so we know that's seven and then that is 16 and then this right over here could be anything it could be 10 it could be 11 it could be 12 it could be 13 it wouldn't change what these medians are wouldn't change this box and whisker plot similarly this could be 13 it could be 14 it could be 15 and so any of those values wouldn't change it and so 75% or 10 or older well this value 6 in this case 6 out of 7 are 10 years old or older and we could try it out with other other scenarios where let's let's try 2 let's try to minimize the number of tens given this data set well we could do something like let's say that we have 8 so let's see 1 2 3 4 5 6 7 8 and so here we know that the minimum we know that the minimum is 7 we know that the maximum is 16 we know we know that the we know that the mean of these middle two values we have an e and we have an even number now so the median is going to be the mean of these two values so it's going to be the mean of this and this is going to be 13 and we know that the mean of we know that the mean of this and this is going to be 10 and that the mean of this and this is going to be is going to be 15 so what could we construct well actually we don't even have to construct to answer this question we know that we know that this is going this is going to have to be 10 or larger and then all of these other things are going to be 10 or larger so this is exactly 75 percent exactly 75 percent if we assume that this is less than 10 are going to be 10 years old or older so feeling very good very good about this one right over here and actually just to make this concrete I'll put in some values here you know this could be this could be a nine and an eleven this could be a twelve and a fourteen this could be a fourteen and a sixteen or it could be it could be a fifteen and a fifteen you could think about it in in any of those in any of those ways but feeling very good that this is definitely going to be true based on the information given in this in this plot now they say there's only one seven-year-old at the party one seven-year-old of the party well this first this first possibility that we looked at that was the case there was only one seven-year-old of the party and there was one sixteen-year-old of the party and actually that was the next date 'men there's only one sixteen-year-old of the party so both of these seems like we can definitely construct data that's consistent with this box plot box and whiskers plot where this is true but could we construct one where it's not true well sure let's imagine let's see we have our median at 13 meeting at 13 and then we have let's see one two three four five one two three four five this is going to be this is going to be the ten the median of this bottom half this is going to be 15 this is going to be seven this is going to be 16 well this could also be seven it doesn't have to be could be seven eight nine or ten this could also be 16 doesn't have to be it could be 15 as well but just like that I've constructed a data set and these could be you know this could be 10 11 12 13 this could be 10 11 12 13 this could be 13 14 15 this cone also it could be 13 14 15 but the simple thing is or the the basic idea here I can have a data set where I have multiple 7's and multiple 16s or I could have a data set we only have one seven or only one sixteen so this both of these statements we just plain don't know we just don't we just don't know now the next statement exactly half the students are older than 13 well if you look at this possibility up here we that we saw that three out of the seven are older than 13 so that's not exactly half three sevens is not one half but in this one over here we did see that exactly half our old are over are older than 13 in fact if you're saying exactly hat well in this one we're seeing that exactly half are older than 13 we have an even number right over here and so it is exactly half so it's possible that it's true it's possible that's not true based on the information given we once again we once again don't we once again do not know anyway hopefully you found this interesting this is the whole point of me doing this is you know when you look at statistics sometimes it's easy to kind of say okay I think it roughly means that and that's sometimes okay but it's very important to think about what types of actual statements you can make and what you can't make it's very important when you're looking at statistics to say well you know what I just don't know that the data actually is not telling me that thing for sure