00:01
All right, so in this question, we are given two data sets for built -up roads and non -built -up roads.
00:06
And we are asked to essentially gauge the variation in those data sets.
00:12
We're asked to figure out which has more variation.
00:15
So the first thing we're going to do, we're going to guess.
00:17
And the second is we're going to calculate the range in the standard deviation and figure out if those match our guesses.
00:24
So firstly, when it comes to guessing, we require a pretty good visual of the data, or at least some sort of idea as to how the data are organized.
00:33
And for this, i have arranged both datasets from least to greatest.
00:37
The reason i can do that, right? in the second dataset, you can see that there are a lot of data points, right, in the 50s, but then it's a pretty big jump to 70, 94, and 102 in particular, right? whereas in the first dataset, the data point seem a little bit more evenly spaced out, and there seems to be a bit of concentration in like the mid to high 80s.
01:03
So i mean if we were to plot these data points, right, maybe this one would have, you know, it'd still be, have some variation, you'd have some big points and some small points, but the small points, right, 69 is nowhere near as small as 53.
01:18
So maybe you would have some sort of plotting like this, right? whereas in the non -built -up data, you would have a lot in the 50s, so a lot quite low down, but then it's a pretty good jump, pretty big jump, pretty big jump.
01:30
So i would argue that indeed, the non -built -up data points have more variation.
01:38
So now let's see if we can verify that with mathematics.
01:42
So first thing that we're going to do is the simplest.
01:44
It's calculating the range, right? well, when we organize it lowest to highest, it makes it very easy because the range is precisely the biggest, minus the smallest.
01:51
So the range for the built -up data is going to be 103 minus 69, which gives us 103 minus 69 is 34.
02:02
So the range here is 34 accidents.
02:06
And for the non -built -up, well, it's the same sort of calculation.
02:10
It'll be 102 minus 53.
02:12
Notice 53 is quite a lot smaller than 69.
02:15
That gives us a range of 49 accidents.
02:17
So indeed, the range for the non -built -up data is quite a bit larger.
02:24
Now when we want to calculate the standard deviation, end, we can do that, right? that's the square root of the sum of the square differences from the mean divided by n minus one.
02:34
I'll write that all out, don't worry.
02:36
But an important part of that is the mean.
02:39
So we need to know the mean of the data set.
02:42
That's just going to be the sum of all of those data points divided by seven.
02:46
So divided by the number of data points.
02:48
We have seven data points, divide by seven.
02:51
When you add all of that up and divide by seven, you will get a mean of 88 .4 accidents.
02:57
For the built -up data.
03:00
Okay.
03:00
Now, when you have that, all right, when you have that, we can calculate the standard deviation...