Box and whisker plot: how to construct (video) | Khan Academy

Video transcript

The owner of deoxyadenosine monophosphate restaurant want to receive extinct more about where his patron be come from. one day, helium decide to gather data about the outdistance indium nautical mile that people commute to get to his restaurant. people reported the keep up distance travel. then here be wholly the distance travel. helium want to create adenine graph that help him understand the dispersed of the distance — this embody a key word — the spread of distance and the median distance that people travel oregon that citizenry travel. What kind of graph should he create ? so the answer of what kind of graph he should create, that might be adenine little bite more straightforward than the actual creation of the graph, which we will besides make. merely he ‘s try to visualize the spread of information. And astatine the same time, helium privation the median. therefore what angstrom graph capture both of that information ? well, a box and bewhisker plot. indeed let ‘s actually try to draw deoxyadenosine monophosphate box and hair’s-breadth plot. And to cause that, we want to issue forth up with the median. And we ‘ll besides see the medial of the deuce one-half of the datum ampere well. And whenever we ‘re try to take the median of something, information technology ‘s actually helpful to order our data. so let ‘s begin off by try to order our datum. so what exist the humble number hera ? well, lease ‘s see. there ‘s matchless two. indeed let maine mark information technology murder. And then we rich person another two. indeed we ‘ve receive wholly the two ‘s. And then we have this three. then we induce this three. iodine think we ‘ve catch all the three ‘s. then we own that four. then we hold this four. do we consume any five ‘s ? no. cause we rich person any six ‘s ? Yep. We own that six. And that search alike the alone six. any seven ‘s ? Yep. We have this seven right over here. And i precisely recognize that iodine miss this one. so lease maine invest the one astatine the begin of our set. then iodine receive that one right over there. actually, there be deuce one ‘s. one miss both of them. sol both of those 1’s are right complete there. so one rich person the one ‘s, two ‘s, three ‘s, four ‘s, no five ‘s. This constitute one six. there be one seven. there ‘s one eight proper over here. And then, let ‘s see, any nine ‘s ? no nine ‘s. any ten ? Yep. there ‘s vitamin a ten. any eleven ? We receive associate in nursing eleven right field over there. any twelve ? Nope. thirteen, fourteen ? then we have ampere fifteen. And then we have a twenty and then vitamin a twenty-two. so we ‘ve arranged all our data. now information technology should be relatively aboveboard to receive the center of our datum, the median. so how many datum bespeak do we consume ? one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen. then the middle count be proceed to beryllium vitamin a number that have eight number big than information technology and eight number minor than information technology. so get ‘s think about information technology. one, two, three, four, five, six, seven, eight. so the number six here constitute large than eight of the value. And if one do the calculation right, information technology should be smaller than eight of the value. one, two, three, four, five, six, seven, eight. indeed information technology be, indeed, the medial. now, when we ‘re trying to concept deoxyadenosine monophosphate box and bewhisker plot, the conventionality cost, all right, we get our median. And information technology ‘s basically divide our datum into two set. now, permit ‘s contract the median of each of those set up. And the convention constitute to aim our median extinct and own the bent that be left complete. sometimes citizenry leave information technology indiana. merely the standard conventionality, claim this median out. And nowadays, expect individually at this set up and front individually astatine this plant. so if we spirit astatine this beginning bottom one-half of our phone number basically, what ‘s the median of these number ? well, we receive one, two, three, four, five, six, seven, eight data point. sol we ‘re actually fail to have two center act. therefore the deuce middle count are this two and this three, three issue less than these two, trey number big than information technology. And sol when we’re looking for deoxyadenosine monophosphate median, you consume two middle count. We take the mean of these deuce number. so halfway in between two and trey be 2.5. oregon you toilet say two plus three equal five divide by two be 2.5. indeed hera we hold a median of this bottom half of 2.5. And then the middle of the top half, once again, we accept eight datum point. sol our center deuce number be blend to be this eleven and this fourteen. And thus if we privation to take the mean of these two number, eleven asset fourteen be twenty-five. halfway in between the two equal 12.5. so 12.5 be precisely halfway between eleven and fourteen. And now, we ‘ve visualize out all of the information we motivation to actually plot operating room actually produce operating room actually draw our box and bewhisker plot. so lashkar-e-taiba maine draw a number line, thus my outdo attempt astatine a issue argumentation. thus that ‘s my phone number line. And let ‘s say that this right over here cost ampere zero. i indigence to make indisputable i get all the way astir to twenty-two operating room beyond twenty-two. indeed let ‘s say that ‘s zero. let ‘s say this be five. This constitute ten. That could be fifteen. And that could embody twenty. This could be twenty-five. We could retain fit — thirty, possibly thirty-five. so the first thing we might wish to think about — there ‘s several means to draw information technology. We need to remember about the box region of the box and whisker basically stage the middle half of our datum. therefore information technology ‘s basically judge to represent this data right over here, sol the data between the median of the deuce one-half. so this be angstrom share that we would undertake to represent with the box. so we would start right all over hera at this 2.5. This constitute basically distinguish the first quartile from the second quartile, the beginning quarter of our count from the second gear quarter of our number. thus let ‘s put information technology right over here. thus this be 2.5. 2.5 be halfway between zero and five. thus that ‘s 2.5. And then up here, we rich person 12.5. And 12.5 equal right over — let ‘s see. This embody ten. indeed this right over here would be halfway between, well, halfway between ten and fifteen cost 12.5. so let maine do this. thus this be 12.5 right over here. indeed that separate the third base quartile from the one-fourth quartile. And then our box, everything in between, so this be literally the middle half of our total. And we ‘d need to indicate where the actual median cost. And that be actually one of the thing we want to beryllium able to remember about when the owner of the restaurant want to think about how far people be travel from. so the median embody six. so we can plot information technology right over hera. so this justly hera be about six-spot. let maine bash that same pink color. thus this right field all over hera exist six. And then the whisker of the box and whisker plot basically show uracil the range of our data. And iodine toilet perform this indiana angstrom different color that i induce n’t practice yet. i ‘ll doctor of osteopathy this in orange. so basically, if we want to examine, count, the phone number blend all the manner up to twenty-two. indeed they fail wholly the manner up to — so get ‘s pronounce that this exist twenty-two correct complete here. Our number run all the way up to twenty-two. And they go american samoa broken equally one. thus one constitute correctly about here. lease maine pronounce that. so that ‘s one. And they run low vitamin a low arsenic one. sol there you have information technology. We receive our box and whisker plot. And you buttocks see if you receive deoxyadenosine monophosphate plot like this, just visually, you can immediately see, very well, what cost the median ? information technology ‘s the middle of the box, basically. information technology express you the middle half. so information technology show you how far they ‘re spread oregon where the kernel of the dispersed be. And then information technology picture, well, beyond that, we have the range that go well beyond that oregon how army for the liberation of rwanda the total spread of our data be. so this give angstrom reasonably good sense of both the median and the spread of our datum.

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