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- [Voiceover] What I wanna do with this video is look

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at some examples of data represented in different ways,

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and think about which representation is the best,

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or can help us answer different questions?

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So we see this first example.

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A statistician recorded the length of each

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of Pixar's first 14 films.

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The statistician made a dot plot, each dot is a film,

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a histogram, and a box plot

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to display the running time data.

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Which display could be used to find the median?

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To find the median.

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All right, so let's look at these displays.

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So over here we see, this is the dot plot.

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We have a dot for each of the 14 films.

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So one film had a running time of 81 minutes.

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We see that there.

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One film had a running time of 92.

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One had a running time of 93.

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We see one had a running time of 95.

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We see two had running times of 96 minutes,

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and so on and so forth.

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So I claim that I could use this to figure out the median,

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because I could make a list of all of the running times

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of the films, I could order them,

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and then I could find the middle value.

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I could literally make a list.

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I could write down 81, and then write down 92,

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then write down 93, then write down 95,

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then I could write down 96 twice,

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and then I could write down 98,

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then I could write down 100.

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I think you see where this is going.

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I could write out the entire list,

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and then I could find the middle values.

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So the dot plot, I could definitely use to find the median.

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Now, what about the histogram?

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This is the histogram right over here.

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And the key here is, for a median, to figure out a median,

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I just need to figure out a list of numbers.

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I need to figure out a list of numbers.

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So here, I don't know, they say I have one film

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that's between 80 and 85,

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but I don't know its exact running time.

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Its running time might have been 81 minutes,

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its running time might have been 84 minutes.

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So I don't know here, and so I can't really make a list

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of the running times of the films

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and find the middle values,

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so I don't think I'm gonna be able

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to do it using the histogram.

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Now, with the box plot right over here,

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so I'm not gonna click histogram.

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With the box plot over here,

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I might not be able to make a list of all the values,

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but the box plot explicitly tells us what the median is.

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This middle line in the middle of the box,

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that tells us the median is, what is this,

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this median is, if this is 100, this is 99.

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So this is 95, 96, 97, 98, 99.

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It explicitly tells us the median is 99.

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This is actually the easiest for calculating the median.

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So I'll go with the box plot.

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So the histogram is of no use to me

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if I wanna calculate the median.

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Let's do a couple more of these.

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Nam owns a used car lot.

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He checked the odometers of the cars

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and recorded how far they had driven.

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He then created both a histogram and a box plot

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to display the same data, both diagrams are shown below.

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Which display can be used

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to find how many vehicles had driven

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more than 200,000 kilometers?

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So how many vehicles had driven

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more than 200,000 kilometers?

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So it looks like here in this histogram,

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I have three vehicles that were between 200 and 250,

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and then I have two vehicles that are between 250 and 300.

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So it looks pretty clear that I have five vehicles,

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three that had a mileage between 200,000 and 250,000,

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and then I had two that had mileage

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between 250,000 and 300,000.

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So I may be able to answer the question.

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Five vehicles had a mileage more than 200,000,

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and so I would say that the histogram is pretty useful.

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But let's verify that the box plot isn't so useful.

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So I wanna know how many vehicles had a mileage

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more than 200,000.

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Well, I know that if I have a mileage more than 200,000,

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I'm going to be in the fourth quartile,

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but I don't know how many values I have sitting there

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in the fourth quartile just looking at this data over here,

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so that's not gonna be useful for answering that question.

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Let's look at the second question.

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Which display can be used

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to find that the median distance,

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which display can be used to find

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that the median distance

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was approximately 140,000 kilometers?

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Well, to calculate the median,

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you essentially wanna be able to list all of the numbers

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and then find the middle number.

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And over here, I can't list all of the numbers.

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I know that there's three values that are

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between zero and 50,000 kilometers,

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but I don't know what they are.

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Could be 10,000, 10,000, 10,000.

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It could be 10,000, 15,000, and 40,000.

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I don't know what they are, and so if I can't list all

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of these things and put them in order,

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I really am going to have trouble finding the middle value.

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The middle value, it's going to be

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in this range right around here,

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but I don't know exactly what it's going to be.

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The histogram is not useful,

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because throwing all the values into these buckets.

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While on the box plot, it explicitly,

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it directly tells me the median value.

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This line right over here, the middle of the box,

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this tells us the median value,

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and we see that the median value here,

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this is 140,000 kilometers.

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Right, this is 100, 110, 120, 130,

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140,000 kilometers is the median mileage for the cars.

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And so the box plot clearly...

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clearly gives us that data.