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Examples analyzing clusters, gaps, peaks and outliers for distributions | 6h grade | Khan Academy - YouTube
Channel: Khan Academy
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- [Voiceover] In this video, I wanna do some examples
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looking at distributions, in particular, different features
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in distributions like clusters, gaps, and peaks.
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So over here, I wanna do some examples.
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Which of the following are accurate descriptions
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of the distribution below?
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Select all that apply.
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So the first statement is the distribution has an outlier.
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So an outlier is a data point that's way off
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of where the other data points are,
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it's way larger or way smaller
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than where all of the other data points
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seem to be clustered and if we look over here,
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we have a lot of data points between zero and six.
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And let's just think about what they're measuring:
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this is shelf time for each apple
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at Gorg's Grocier.
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So, for example, we see there's one, two, three, four,
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five, six, seven apples that have a shelf life
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of zero days, so (laughs), they're about to go bad.
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You see you have one, two, three, four, five, six, seven,
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eight apples that are gonna be good for another day.
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You have two apples that are gonna be good
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for another six days, and you have one apple
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that's gonna be good for 10 days, and this is unusual.
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This is an outlier here, it has a way larger shelf life
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than all of the other data, so I would say
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this definitely does have an outlier.
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We just have this one data point
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sitting all the way to the right, way larger,
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way more shelf life than everything else, so it definitely
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has an outlier, and this one would be the outlier.
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The distribution has a cluster from four to six days.
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And we indeed do see a cluster from four to six days.
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A cluster, you can imagine, it's a grouping of data
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that's sitting there, or you have a grouping of apples
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that have a shelf life between four and six days,
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and you definitely do see that cluster there.
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And since I already selected two things,
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I'm definitely not gonna select none of the above.
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Let me check my answer.
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Let me do a few more of these.
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Which of the following are accurate descriptions
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of the distribution below?
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And once again we're going to select all that apply.
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So the distribution has an outlier.
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So let's see this distribution.
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I do have a data point here that is at the high end
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and I have another data point here that's at the low end,
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but I don't have any data points that are sitting
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far above or far below the bulk of the data.
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If I had a data point that was out here, then yeah,
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I would say that was an outlier to the right,
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or a positive outlier, if I had a data point way to the left
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off the screen over here, maybe that would be an outlier,
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but I don't really see any obvious outliers.
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All of the data, it's pretty clustered together.
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So I would not say that the distribution has an outlier.
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The distribution has a peak at 22 degrees.
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Yeah, it does indeed look like we have,
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and let's just look at what we're actually measuring:
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high temperature each day in Edgeton, Iowa in July.
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So it does indeed look like we have the most number
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of days that had a high temperature at 22,
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most number of days in July had a high tempurature
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at 22 degrees Celsius, so that is a peak.
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You can see it, if you imagine this as kind of a mountain
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this is a peak right here, this is a high point.
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You have, at least locally, the most number of days
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at 22 degrees Celsius.
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So I would say it definitely has a peak there.
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Since I selected something, I'm not gonna select
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none of the above.
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Let's do a couple more of these.
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Which of the following are accurate descrptions
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of the distribution below?
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So the first one, the distribution has an outlier.
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So...
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number of guests by day at Seth's Sandwich Shop.
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So, let's see, the lowest...
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They have no days...
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No days where he had between zero and 19 guests,
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no days where he had between 20 and 39 guests,
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looks like there's about nine days
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where he had between 40 and 59 guests,
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looks like 20 days where he had between 60 and 79 guests,
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all the way where it looks like maybe 8 days
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that he had between 180 and 199 guests.
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But the question of outliers, there doesn't seem to be
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any day where he had an unusual number of guests.
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There's not a day that's way out here,
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where he had, like, 500 guests.
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So I would say this distribution does not have an outlier.
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The distribution has a cluster from zero to 39 guests.
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So zero to 39 guests is right over here, zero to 39 guests.
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And there is no days where he had between zero and 39 guests
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neither zero to 19, or 20 to 39.
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So there's definitely not a cluster there.
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I would say that the cluster would be between days
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that had between 40 and 199 guests.
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Definitely not zero and 39, there was no days
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that were between zero and 39 guests.
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So I would say none of the above very confidently.
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Let's do one more of these.
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Which of the following are accurate descriptions
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of the distribution below?
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(laughs) Alright.
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The distribution has a peak from 12 to 13 points.
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Let me see what this is measuring, what this data is about.
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Test scores by student in Mrs. Frine's class.
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So you had one student who got between a zero and a one
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on a 20-point scale, so got between,
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I guess out of 20 questions, got between zero and one point.
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And then you see that there's no students got
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between two and three, or four and five, or six and seven.
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Then we have another student who got between eight and nine,
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looks like three students got between 10 and 11,
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and then we keep increasing, this looks like about
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12 students got either a 16 or a 17,
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or something in between maybe,
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if you could get decimal points on that test.
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And then it looks like 10 students got from 18 to 19.
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Alright, so this says the distribution has a peak
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from 12 to 13 points, 12 to 13 points,
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there were five students, but this isn't a peak.
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If you just go to 14 to 15 points, you have more students.
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So this is definitely not a peak.
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If you were looking at this as a mountain of some kind,
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you definitely wouldn't describe this point as a peak.
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You would say this distribution has a peak,
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it has the most number of students
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who got between 16 and 17 points,
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so that's the peak right there, not 12 to 13 points.
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So I would not select that first choice.
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The distribution has an outlier.
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Well, yeah, look at this: you have this outlier.
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Most of the students scored between eight and 19 points,
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and then you have this one student
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who got between zero and one, it's really an outlier.
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You even see this when you look at it visually,
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it's not even connected to the rest of the distribution.
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It's way to the left.
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If something is way to the left or way to the right,
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that's an outlier if it's unusually low or unusually high.
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So I would say this distribution definitely does
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have an outlier, and I'm not gonna pick none of the above
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since I found a choice.
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And I think we're all done.
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