00:01
This problem is a problem about turning raw data into something more visual so that you can actually see patterns or things that are unusual, things that you might not be able to see if you don't have your data in some kind of graph.
00:18
So you're being given a bunch of times, 57, actually, to count them up, 57 different times.
00:26
So i'm just going to make a note here that we have 57 different pieces of.
00:31
Data so n is equal to 57 that represent the time that it takes for bobsleds to finish a race okay so the first thing that you're asked to do is to divide this into five classes so five categories to break this down so for the class width what we're going to do is just take the highest value of 360 minus the lowest value of 236 and we're going to divide that into five equal parts all right, well, it turns out that that is 24 .8, which is kind of an awkward number to use.
01:09
So we're going to round that up to 25.
01:13
You could round it up to 30, but the more you round, the less accurate your graph is going to be.
01:21
So we know that we have class widths of 25.
01:25
Now, what you'll notice about the data that i have at the top is that i already put all of the data into numeric.
01:31
Order.
01:33
I happened to do it with excel.
01:35
It's a bit tedious if you don't import all the data into excel, but it's certainly doable.
01:43
And so now we're ready to figure out what the categories or the classes look like.
01:48
So the lowest category is going to start at 236, and then i'm going to add 25.
01:56
So i end up getting, sorry, 261.
02:05
I'm going to to add 25 again and i get 286.
02:10
Add 25 again, i get 311, and one more time i get 336.
02:19
Okay, so those are the lower limits of each class.
02:23
Now, the upper limit is easy to figure out.
02:25
This is going to go from 236 to 260, just before i hit the next class.
02:31
261 to 285, 286 to 310, 311 to 335, and then the next class after 336 would actually be 361, although i'm not going to end up using that, but it does tell me that the high end is 360.
02:55
So you might just want to take one second and make sure that your classes will fit all.
03:01
The data that you've done it correctly so that they all fit and we don't have to go any higher than 360 so we're all set.
03:09
All right, class boundaries.
03:11
So i'm going to go across just one class for right now and this is the class that i have in green up above.
03:18
So just four pieces of data.
03:20
So actually i'll go ahead and put that in under the frequency.
03:24
There's four pieces of data.
03:26
All right, the class boundaries, the rule for the class boundaries is that you're just going to go from 0 .5 below the low boundary.
03:36
So that would be 235.
03:40
And you're going to go to 0 .5 above the higher boundary.
03:46
So we're going to say that the boundaries go from 235 .5 to 260 .5.
03:53
And these boundaries are what you're going to use when you make your graphs.
03:59
Okay, so these are going to be used for the purpose of making your graphs.
04:04
You'll see that in a little bit.
04:06
All right, midpoint should be fairly straightforward.
04:08
We're just going to take the average of 236 and 260.
04:13
So 236 plus 260 divided by 2 is going to give me 248.
04:20
Okay.
04:21
The relative frequency is just the frequency divided by the total.
04:28
And then you're going to want to turn that into a percent or a decimal.
04:34
If it's approximate, that's completely fine.
04:36
So this would be, if you do that in your calculator, it's about 7%, but i'll leave it as a decimal.
04:42
And then the cumulative frequency, that refers to the number of pieces of data you have so far.
04:50
So by the time you get to 260, how many pieces of data have you accumulated? and we've accumulated only four.
04:59
All right okay i'll do one more row kind of talk through it and then i'll show you the rest without going through all of them okay so here's the next row so notice that um the boundaries are 0 .5 below and 0 .5 above the class limits the midpoint comes from adding 261 plus 285 taking that entire quantity and dividing by two.
05:31
Okay, the frequencies come from going back to looking at the raw data and just counting the number of pieces of data that fall between 261 and 285.
05:44
And if i count those up, one, two, three, four, five, six, seven, eight, nine.
05:49
Okay, the relative frequency is just nine divided by the total, which i'm going to round to about 16%.
05:58
And now, by, by the time i've gotten to 285, i've accumulated a total of 13 pieces of data.
06:09
So it's really just my original four plus the nine that were in this category.
06:17
All right, filling out the rest of the table.
06:21
I'm just going to go ahead and put this up there.
06:25
The one thing that i think might bear looking at are the cumulative so by the time i get to 310, i have accumulated the original 4 plus the 13, and now i've accumulated 25 more.
06:53
So if i do, oh, sorry, the 4 plus the 9 plus the 13.
06:58
So let me go back just for a second here.
07:00
So it was my original 4, which was here.
07:06
Then the nine that i got from the second category, and then finally the 25 that i got from the third category.
07:15
And that gives me a cumulative of 38.
07:19
The other way you can do it is just take the previous category and add on the amount in that category.
07:28
So we started with 13 from the previous two.
07:31
We added 25.
07:32
Okay.
07:34
We started with, for the next one, we started with 38 and we added another 16 in that category.
07:44
Okay.
07:44
And then finally, we started with 54 and added another three in this category to get a total of 57.
07:56
And it is worth checking.
07:58
By the time you get to the end here, you should have the total of, the number of pieces of data.
08:05
So if you ended up, for example, with 56, you would know that you added something wrong along the way.
08:12
All right, that's kind of the tedious part.
08:15
Now, putting this into a picture, that's the part that's a little bit more interesting.
08:19
So, first of all, when i make a histogram, i want you to notice that the class boundaries are what i use on the x -axis.
08:30
Right? another thing to notice is that you always want to label your axis, both of your axes.
08:37
So these are finished times to the nearest hour.
08:41
And then along the y -axis for a histogram, i'm going to use the frequencies.
08:49
So just how many pieces of data were in each category.
08:54
So that would be this column right here.
08:58
This is the column i'm going to use for histograms.
09:06
All right.
09:06
And then it's just a question.
09:07
Of plotting the various points.
09:10
So we know that from 235 .5 to 260 .5, we had four pieces of data.
09:16
So, oh, sorry.
09:18
And then the other thing that we need to do is label the y axis.
09:22
So we know we're going all the way up to the highest frequency is 25.
09:26
So i set this out so that it would be easily divisible, and i'm just going to go 5, 10, 15, 20, 25.
09:36
Okay, so then first class.
09:38
We had four, so i'm just going to kind of eyeball this, and we draw a bar.
09:48
The second one, we had nine.
09:50
So again, this just can be pretty approximate.
09:57
Third category, that was the big one.
09:59
We had 25, so we're jumping all the way up to here, and then drawing a bar all the way down.
10:09
Fourth category, we had 16, so that's that bar there.
10:19
And last category we had three.
10:25
So we're back down to just a few.
10:28
So put that at three.
10:30
And there's your histogram.
10:33
Now, a relative frequency histogram is very, very similar.
10:38
It's just that you have different values on the y -axis.
10:45
And these, instead of being the actual number, is going to be the percent...