The cholesterol levels in milligrams per deciliter of 30...

'The cholesterol levels (in milligrams per deciliter) of 30 adults are listed below. Draw box-and-whisker plot that represents the data _ 154 156 165 165 170 171 172 180 184 185 189 189 190 192 195 198 198 200 200 200 205 205 211 215 220 220 225 238 255 265 a. Find five-number summary for this data b: Draw boxplot that represents the data above: Please state and label the lower limit; upper limit: Label any outliers if any.'

Transcript

00:01 So we're looking at the cholesterol levels of 30 different adults.

00:05 And we want to use this data to create a box and whisker plot and draw some other conclusions based on the data.

00:12 So i've organized the data to split it in half, 15 on the top row, 15 in the bottom row, from smallest to largest, which was already given to us.

00:21 And this is going to help us come up with a five number summary for the data.

00:27 There are five numbers we want to come up with, obviously.

00:30 The first one is the minimum, and the minimum is just the smallest number, which is 154.

00:39 The next number is our maximum.

00:42 Let me mark something.

00:43 See, here's our minimum, 154.

00:46 Our maximum is just the other end of the spectrum, 265.

00:57 265.

00:59 And then the middle number is the median.

01:04 And the median, because we have an even number of.

01:08 Numbers is actually right in between 195 and 198.

01:18 So to find that, we can just basically find the middle of those two middle numbers.

01:23 So instead of 195 or 198, it ends up being 196 and a half.

01:33 So our median is 196 and a half.

01:38 Now we have two more numbers that we have want to come up with here.

01:42 The first one is the lower core tile or q1 and that represents like the first 25 % of the data.

01:57 So it's sort of like the median of the bottom of the bottom half of the data.

02:02 And then the second one is the upper core tile, which is just the other side of it.

02:06 It's like the 75th percentile or the median of the larger or the largest number.

02:14 Sorry.

02:14 Right, the median of the other half of the data, like the larger numbers.

02:20 So we can do that just by finding our middle of this top row.

02:26 So the median of our top row is 180.

02:30 That would be our lower core tile.

02:34 And the meeting of the upper half or the upper quartile is 211.

02:41 You can see why it's beneficial to organize the data in this way, because there's a lot of symmetry as you are looking through all the numbers.

02:51 And so it's pretty easy to spot where these numbers are going to be.

02:54 So here's our five number summary.

02:56 The minimum is 154, maximums 265, median 196 .5, lower quartile is 180, and upper quartile is 211.

03:06 That gives us a great start for us to come up with our box and a whisker plot.

03:14 So let's draw out a bit of a number line at the bottom just to give ourselves some some points to kind of think about and we know we're going to be going from 154.

03:29 So let's start down at like 150 down here at the bottom 150 and we're going to go all all the way up past 265.

03:42 So let's try going by, i don't know, maybe 20 at a time or something like that.

03:50 It doesn't really matter.

03:51 It's just to help us kind of gauge where some of these numbers are going to be.

03:56 Let's say you just go by tens.

03:57 That's fine.

03:58 So here's 160, 170, 180, 190.

04:06 Actually, let me start over.

04:07 I apologize.

04:11 The reason i'm starting over here, is i'm going to kind of put my number down right in the middle so i can say, okay, this is about 200.

04:20 So there's 200.

04:22 And now i can break things up into 160, 170, 180, and 190.