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# Worked example: Creating a box plot (odd number of data points)

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

## Video transcript

I represent the following data using a box and whiskers plot exclude the median when computing the quartiles all right let's see if we can do this so we have a bunch of data here and they say if it helps you might drag the numbers to put them in a different order so we can drag these numbers around which is useful because we will want to order them the order isn't checked with their X with your answer that I'm doing this off of the Khan Academy exercises so I don't have my drawing tablet here I just have my mouse and I'm interacting with the exercise which I encourage you to do too because the best way to learn any of this stuff is to actually practice it and it kind of can we have 150,000 exercises for you to practice with anyway so let's do this let's order this thing too so we can figure out the range of numbers what's the lowest and what's the highest so let's see there's a seven here and then let's say we have some eights we've got some eights going on and then we have some nines actually we have a bunch of nines we have four nines here there's some nines and then let's see thirteen is the largest number there we go we've ordered the numbers so our smallest number is seven and this is what the whiskers are useful for for helping us figure out the entire range of numbers our smallest number is seven our largest number is 13 so we know the range now let's plot the median and this is this will help us once getting this center line of our box but then also we need to do that to figure out what these other lines are that kind of define the box to define the middle two fourths of our number of our data or the middle two quartiles roughly the middle two quartiles it depends how some of the numbers work out but this middle number this middle line is going to be the median of our entire data set now the median is just the middle number if we sort them in order median is just the middle number we have 11 numbers here so the middle one is going to have five on either side so it's going to be this nine if we had if we had ten numbers here if we had an even number of numbers you actually would have had two middle numbers and then to find the median you'd have found the the mean of those two if that last sentence was confusing watch the videos on Khan Academy on median and I go into much more detail on that but here I have 11 numbers so my median is going to be the middle one it has five larger five less it's this nine right over here if I had my pen tablet I would circle it so it's this nine that is the median and now we need to figure out well what number is halfway or let me put it this what number is the median of the numbers in this bottom half and they told us to exclude the median when we compute the quartiles so this was the median let's ignore that so let's look at all the numbers below that so this nine eight eight eight and seven so we have five numbers what's the median of these five numbers well the median is the middle number that is eight so the beginning of our second quartile is going to be an eight right over there and we do the same thing for our third quartile remember this was our median of our entire data set let's exclude it let's look at the top half of the numbers so to speak and there's five numbers here in order so the middle one the median of this is ten so that's going to be the top of our second quartile and just like that we're done we have constructed our box and whisker plot