00:01
So you're given a set of data and you need to do a number of things with that data.
00:07
And it'll be easier if you put all of the data into a graphing calculator.
00:12
So i'm going to hit my stat feature, edit, and as you can see, it's already in my calculator.
00:19
Now having it in ordered, smallest to largest would also help.
00:25
So that's the next thing i'm going to do.
00:26
So i'm going to quit out of here.
00:28
I'm going to hit stat.
00:29
And i'm going to select number two to sort my list and i want it in ascending order.
00:38
So now it's done.
00:40
So we are ready to take a look at our list, but this time, as you can see, the smallest number is on the top and the largest number is on the bottom.
00:51
All right, so we're ready to begin then.
00:54
Part a, you have to identify the class with.
01:03
And in order to do that, you're going to take the maximum piece of data minus the minimum piece of data, and you're going to divide it by the number of classes.
01:19
So in this particular set of data, our highest number is 79.
01:27
Our lowest number is 26, and we want to categorize our information into five classes.
01:36
Now when i do that, i get 53 over 5 or 10 .6, and what i'm going to do is i'm going to round that up to the next integer.
01:47
And it wouldn't matter what that value was.
01:50
It could have been 10 .2.
01:52
Either way, i'm going to always go up to the next integer.
01:55
So my class width is going to be 11.
02:00
Now, part b.
02:02
Part b, you're going to create a frequency distribution.
02:07
And not only are we going to create a frequency distribution, we're going to extend it beyond the most basic.
02:15
So we need to determine class limits, then we need class boundaries, we need to define the midpoint of the class, we need to find the frequency of the class, we need the relative frequency, and then we need to incorporate the cumulative frequency.
02:55
See.
03:05
All right, so let's start with the class limits.
03:08
To determine our class limits, you're going to start with the minimum value, and we already said our minimum value was 26.
03:18
And we just determined our class width to be 11.
03:23
So that means we need 11 numbers in that class.
03:27
So we're then going to take that 11, and we'll add it to the 26 to find the lower class limit of the second class.
03:36
And then we're going to add 11 to that to find the lower class limit of the third class.
03:42
And continue doing that until we have the five classes.
03:48
Now we need the upper class limit of each.
03:52
Well, if the first one starts at 26 and we need 11 numbers in there.
03:59
So if i were to count 26, 27, 28, 29, 30, 31, 32, 33, 33, 34, 35, 35, 36 would be 11 numbers.
04:09
So the first class has to end at the integer just before where the second class would start.
04:18
So since the third class starts at 48, this means the second class would have to end at 47.
04:26
And since the fourth class begins at 59, the third class would have to end at 58.
04:33
And then the same thing.
04:36
This would have to end at 69.
04:38
And this would have to end 11, because our class width was 11, 11 numbers later, which would put us to 80.
04:51
Now we're ready to talk about our class boundaries.
04:55
Now our class boundaries is to help us ensure that when we draw histograms, our towers indeed touch.
05:02
So what you're going to do is you're going to take each of the numbers in the lower class limit position and back it up by a half.
05:10
So this will be 25 .5, 36 .5, 47 .5, 58 .5, and 69 .5.
05:27
And then you're going to take the upper class limits, and you're going to add a half.
05:30
So now this is going to be 36 .5, 47 .5, 58 .5.
05:38
58 .5.
05:42
169 .5, and 80 .5.
05:48
And again, the purpose of those class boundaries is so that when we create our histogram, we end up with towers that touch.
05:58
Now to find our midpoint, we're going to use the formula, max plus min divide by two, which means we're taking the maximum of the class, we're adding it to the minimum of the class, and we're going to then take that sum and divide it by two.
06:26
So for this first one, i would take 26 plus 36 and divide that by two, and i end up with a value of 31.
06:51
So therefore, i've got a 31.
06:54
And i'm going to do that 37 plus 47 and divide by 2, and i'll get 42, and i'll do the same.
07:03
Thing for the third class, 48 plus 58, divide by 2, will get me 53.
07:10
And then i'll do 59 plus 69, and divide by 2, we'll get 64.
07:17
And then 70 plus 80, divide by 2, result in a midpoint of 75.
07:24
So now we're ready to do our frequency.
07:27
And to do our frequency, the easiest thing to do would be to go back to our graph and calculator, now that the data is in order, and for the first class, we're looking for numbers that are anywhere from 26 to 36 inclusive.
07:44
And if i look at my graph and calculator, i could see that there are four numbers that are in the class 26 to 36.
07:55
And then i'm going to look for 37 to 47.
07:58
And as i look from 37 to 47, and as i look from 37 to 47, and count them, i'm going to find that there are 21 numbers.
08:09
And then for the class 48 to 58, again, i'm going to count them from 48 all the way down to 58 would be 22 different numbers that could fall in that class.
08:24
59 to 69, i could see that there's only one number.
08:30
And then 70 to 80, i could see that there are two numbers.
08:38
The next is going to be our relative frequency.
08:44
And to find relative frequency, you're trying to find a part over a whole.
08:51
So if i were to add up my frequency, i know there were 50 numbers in that set of data.
09:03
So my relative frequency is what part of the numbers were in the 26 to 36 class? and there happened to be four out of those 50 numbers.
09:16
And as a decimal, that would translate into 0 .08.
09:23
What part of the numbers fell in the second class? well, there were 21 numbers out of 50 numbers.
09:30
So that would translate as a decimal into 0 .42.
09:37
In the third class, there were 22 numbers out of the 50 numbers, which would be 0 .44.
09:45
In the fourth class, there was 1 out of the 50 numbers, so that would be 0 .02.
09:54
And then finally, in the fifth class, there were 2 out of the 50 numbers, were in that fifth class, which would be 0 .02.
10:04
So now we're ready to do the cumulative frequency.
10:12
For cumulative frequency, we're going to add the frequency in the class and any previous class.
10:21
So the only number in the first class is four, and there's no previous class, so that frequency would be four.
10:28
But to find this frequency, we're going to take the frequency of the class plus any previous class.
10:36
So we're adding the 21 and the 4, so we are going to get a value of 25.
10:48
And then for the third class, we're adding the 22 in this class plus the 21 in the previous class, plus the 4 in the previous class.
10:58
So when i add those three values up, i'm going to get 47.
11:05
Now for the cumulative frequency for the fourth class, i'm taking the one that was in the class, adding it to the 22...