00:01
Once again, welcome to a new problem.
00:04
One of the things that happens in statistics is the fact that you have to describe data.
00:12
And a couple of ways of describing data, one of the things you have to know is that there are two ways you can describe data.
00:21
So there are two branches of statistics, not two ways you can describe data.
00:26
So there are two branches.
00:28
Is the first one is descriptive statistics, and then the second one is inferential statistics.
00:39
And so on the descriptive part, we have a problem where we're given data.
00:45
So there's a range of data values that you're given.
00:48
So you have 27, you have 25, you have 20, you have 15, you have 30, you have 34 and then you also have 28 and then 25 so the goal of this problem is to figure out what the range is the inter quartile range into quartile range you also have the variance and then you have the standard deviation so that's the requirement for the range remember this is the gap between the highest and the lowest value.
01:44
That's the gap.
01:45
The inter -quarter range is also a gap between q1 and q3.
01:52
Of course, q1 is the first quartile.
01:56
If you organize the data from the lowest to the highest, and then q3 is the third quartile.
02:05
Q3 is the third quartile.
02:08
So the interquarter range is a different between those two numbers.
02:15
The problem with the range is that it's affected by skewed data, and then the interquotar range, like the median, is not affected by skewed data.
02:28
The variance is a computational tool used to determine the standard deviation, which is the average deviation from the mean.
02:46
So these are the requirements of the problem.
02:49
And the first thing we're going to do is organize the data from the highest to the lowest.
02:56
So the lowest is 15, and then we have 20, and then of course we have 25, and 25 is going to happen two times.
03:10
So we have 25 there and 25 there.
03:13
And then we have next to 25, we have 27 and of course we have 28.
03:20
We have 27 and 28.
03:24
And then to round it off, we have after 28, we have 30.
03:31
And then we also have 34.
03:35
This is the range of numbers that you're dealing with.
03:38
So the first part is to compare the lowest value.
03:43
The highest value and the lowest value to get the range.
03:51
So this is going to be highest minus lowest, which is 34, minus 15.
04:04
And so we have a range of 19.
04:08
That's the first part of the problem.
04:11
Second part is that given these numbers, we have to compute given these numbers we have to compute the the inter -quarter range iqr so the way you do it is you look at the first quartile so iqr is the difference between the third quarter in the first quarter we have a couple of items here we have one two we have one two three four five six seven eight we have eight items.
04:53
The median is the fourth and the fifth right there.
04:59
And then, of course, we're going to look at another pair, second pair.
05:08
So you have different quartels if we have eight positions.
05:13
If we have eight positions, the middle is eight over two, which is four.
05:20
So this splits in the middle.
05:23
And then of course we need to get the middle of these four items and that's going to fall between these two, 20 and 25.
05:33
And then the next middle of these other four items will fall right here, 28 and 30.
05:41
And so we end up having q1 is the same as 20 plus 25 over 2.
05:53
Q1 is 20 plus 25 over 2.
05:59
I want to simplify this.
06:04
So q1 becomes 20 plus 25 over 2, which is 45 over 2, that's 22 .5.
06:13
And then q2, or rather q3, becomes 28 plus 30, all over 2, which is 58 over 2.
06:26
And that's going to give this 29.
06:30
So then, of course, to get iqr.
06:34
We're taking 29 minus 22 .5 which ends up giving us an iqr of 6 .5.
06:47
So this is going to be an iqr of 6 .5 and we're looking at positions.
06:53
So this is q1 falls right here and then q2, q3 falls right here.
07:03
Of course q2 which is the median is going to fall right there.
07:06
It's a q2.
07:07
So the second part of the problem, the third part of the problem is we have to compute the variance.
07:17
So we need a table.
07:19
The x values are the values that were given.
07:23
So we had 2 .25s.
07:27
We had a, well, actually 225s.
07:30
We had 20 or 15 and a 20.
07:34
I don't know why i started off like the 225s.
07:37
I guess i just liked them.
07:39
So we had a 15 and a 20 and then we had 2 25s.
07:43
So that's already four items.
07:47
And then we had 27 and 28.
07:52
And then finally we had 30 -34.
08:01
First step is to get the deviation from the main, but we don't have the main yet.
08:05
So we have to compute the main, which is summing up all these values and dividing by n.
08:10
If you sum up all those values, you can see we get, 204 and then of course n is 8 and that's going to give us 25 .5 that's the mean.
08:23
We want to get the deviation from the mean for all these values.
08:26
So we have 15 minus 25 .5 and then we have 20 minus 25 .5 and then we have 25 minus 25 .5.
08:36
And then we have another 25 minus 25 .5 .5.
08:39
We have 27 minus 25 .5 .5.
08:42
We have 28 minus 25.
08:45
And then of course we have 30 minus 25 .5 and we have 34 minus 25 .5.
08:55
That's the next step.
08:58
We're going to get the differences between these so all the differences we're going to place it there and then square the result.
09:10
So this would be x minus x bar and square that...