00:01
All right.
00:01
So for this data set, we have the speeds of 30 motorists, and we want to construct a few different things.
00:13
We want to make a frequency distribution, a relative frequency distribution, and a cumulative frequency distribution using six classes.
00:22
And then we also want to construct a histogram of frequency and relative frequency, also using six classes, as well as a stem and leaf plot of these data.
00:36
So the first thing that i did was just order the numbers.
00:40
These are the speeds in miles per hour of those passing cars.
00:43
And i ordered them in ascending order from least to greatest.
00:49
And by doing this, this will help us better organize our histogram when we go to make it.
00:56
And so now to find our classes, since we need six even classes, we're going to find the range of these numbers first.
01:08
So we're going to do the greatest number minus the smallest number.
01:11
And that gives us 17.
01:13
So there are 17 points between the smallest and largest number here.
01:17
And if we want to find six even classes, we'll divide it by six.
01:22
And then we get 2 .83.
01:26
And so we're going to use this as our width of each of the classes.
01:32
So we can start then at the bottom at 33 and then add 2 .83 to each class.
01:40
So that gives us an even width.
01:42
And then we'll just work our way up from there.
01:45
So let's go ahead and do that.
01:47
And we'll just write these out.
01:48
So the first one will be 33 to 35 .83 and then 35 .83 to 38 .67 and then 38 .67 to 41 .5 to 44 .3 and then 47 .16 to 50 .15 to 50.
02:13
And so here are our classes.
02:15
They all have an equal width.
02:18
And now we are going to count the number of observations that fall within each of these classes.
02:27
And so that's why i said it was helpful if we organized our data in ascending order.
02:32
And that way we can just go down the row and put a bracket around what fits into each class.
02:38
So 33 through 35 all fall within this first class here.
02:44
And we'll just write the number out because that will help us with our relative frequency.
02:47
Distribution that we are going to make.
02:50
And then the next six, and then the next six, and six again, and then three, and then six.
02:58
So these are our classes, and we're basically now just going to create a y axis that goes up to six, so we can plot all of our points on there.
03:10
And then i'm just going to use an x as my histogram marker.
03:15
This might look differently depending if you're using a software or if you're doing this by hand.
03:21
And so i'm just going to mark all the way up into that line.
03:25
So this group has six.
03:27
So i'm going to go all the way up to the six.
03:29
And then again, again, these could be boxes.
03:33
These could be dots.
03:34
These could be whatever you want.
03:36
These could be bar lines.
03:38
And so now that we have our histogram, we can use this to create our frequency.
03:46
Polygon.
03:49
And basically a polygon is just when we would connect the dots between all of our points...