00:01
Okay, so here we have some summary statistics that i wrote down here that basically describe what percentage of freshman year to graduate on time in four years.
00:14
So we need to describe, you know, what type of distribution we got or what, like, what type of the shape is.
00:21
So we want to describe it, is it like symmetric? can we say it's more symmetric or can we say it's more skewed? and then we need that and find any outliers and make a box plot and write a couple sentences.
00:30
So i'm kind of going to do all these all these parts together because they help one another.
00:35
So um, let's start by making the box plot because that lets you see the shape and lets you see outliers and stuff like that.
00:42
So remember a box plot is made by taking the five number summary.
00:48
So the men, the first quartile, the median, the third quartile, and then the max.
01:05
And so the minimum we got to be 43 .2.
01:11
So we'll start there.
01:14
And we're gonna draw a whisker or a line up to the first quartile, which is the same as the 25 percentile, which we've got to be 59 .15.
01:26
Make it a little farther actually.
01:33
59 .15.
01:35
Then we're gonna draw a box around q1 to q3.
01:40
So we're going to draw a box out here and align at the median, which is 69 .9.
01:52
So here's our median.
01:56
And then we draw the third quartile is 74 .75, which will be kind of close.
02:02
So over here, 74 .75.
02:07
And then we draw our final whisker up to the max.
02:11
Max was about or it is 87 .4 there's a rough sketch of our box plot now to figure out if there are any outliers what we want to do actually they actually do a different color outliers a common rule to use is the 1 .5 times iqr the 1 .5 iqr so the 1 .5 iqr rule basically says that if you can find values that are more than 1 .5 iqr units above q3 or more than 1 .5 iqr units below q1, then those will count outliers.
03:07
So the iqr, let's recall, is basically a distance from q1 to q3, or you can basically take q3 minus q1.
03:16
So 74 .75 minus 59 .15 and we get 15 .6 oops so so 50 backtrack right over here so our iqr is 15 .6 so the 1 .5 iqr rule means you got to take 1 .5 and multiply it by 15 .6 and we get 23 .4 and that's gonna be our magic number.
04:21
We wanna see, are there any values in this distribution that are 23 .4, or that are more than 23 .4 units away from q3 and below q1.
04:34
So what we do is gonna take, we're gonna take q3, which is 40, or which is 74 .75, and add 23 .4 to it and we get 98 .15.
05:09
So we have no values that are above 98 .15.
05:14
So we have no outliers in this direction.
05:18
Now we got to check the other direction.
05:19
We got to check if it's 23 .4 units or more below 59 .15.
05:26
So we're going to be 59 .15 minus 23 .4.
05:29
4 and we're going to get 35 .75 and we don't have any values below 35 .75 either...