Lesson video

In this lesson, we're going to learn how to plot to cumulative frequency diagram.

Cumulative may be a new word to you, but you may know the word accumulate, which means to gather together or build up.

Or you may know about cumulus clouds, the big fluffy white ones, where the water vapour is all gathered together and built up.

Cumulative frequency means that the total so far or a running total.

And we can find it using the frequency.

So let's have a look at this example, the total rolls of ribbon, which are five metres or less is eight.

So the entry in the first position in the cumulative frequency column is the same as that of the frequency column.

Now the next entry will be the total of all the ribbon reels that are 10 metres or less.

So we would add eight and 15 together to give us 23.

And the next entry is all those that are 15 or less.

So we would add together eight and 15 and 26.

But we already know eight and 15 is 23.

So just add 26 onto that.

And that gives us 49.

And then to get the next entry we add on 23, which is 72.

And finally, we add on eight, which gives us 80.

Do you notice that in the question it told us that there were 80 reels of ribbon.

And our final entry in the cumulative frequency column is the total frequency.

So that double checks that we've done all our arithmetic right.

Now we can draw a diagram from this.

We're going to plot some coordinates using the upper bounds on the cumulative frequency.

We use the upper bounds 'cause remember when I was taking you through the table, I talked about it being five or less, 10 or less and so on.

So let's plot five eight.

Let's now plot 10, 23.

Then, 15, 49.

20, 72, and finally 25, 80.

And we can draw a smooth curve through this.

This is a cumulative frequency diagram.

Here's a question for you to try.

Pause the video to complete the task and restart the video when you're finished.

Here are the answers.

Did you notice that the first value in the cumulative frequency column is always the same as the first value in the frequency column? And the final volume in the cumulative frequency column is always the total frequency.

And with questions like this, where that information is actually given in the introductory text, it can be really useful for checking that we've not made any arithmetic errors.

So what else for the modal class? And this is just another way of saying which class interval is the mode.

Now, some people do fall into the trap of maybe giving an answer of 12 here.

So 12 tells us, which has the highest frequency 'cause 12 is greater than all the other frequencies in this example, but that's attached to the class interval, 10 to 20.

So, that is the true answer, not 12.

Here's another question for you to try.

Pause the video, to complete the task and restart the video when you're finished.

Here are the answers.

We always plot upper bounds against cumulative frequency and joining the points with a smooth curve is not easy, but that will improve greatly with practise.

Here's a further question for you to try.

Pause the video to complete the task and restart the video when you're finished.

Here are the answers.

This can be a common error, particularly because midpoints are used when we plot frequency polygons, or we also use midpoints when calculating the estimate mean of a group frequency distribution.

In this example, we'll be working from a completed cumulative frequency diagram in order to complete a cumulative frequency table.

So we'll fist look at the coordinates of the points where the upper bound is the X coordinate.

And this will help us find the Y coordinate, which is the cumulative frequency.

Then we'll be able to complete the frequency column.

The first coordinate on our curve is 24.

So we've placed four in that first position on the cumulative frequency column.

Then we have 40, 12, 60, 29, 80, 36 and 140.

Now we remember from before that the first entry in the frequency and cumulative frequency columns are the same.

This is far.

Now all we need to do is work our way down the cumulative frequency column, looking at the differences between the entries.

So from four to 12 is a difference of eight.

From 12 to 29, it's a difference of 17.

From 29 to 36 is seven.

And finally from 36 to 40 is four.

Here's a question for you to try.

Pause the video, to complete the task and reached out the video when you're finished.

Here are the answers.

Thinking about the fact that the first two values in the frequency and cumulative frequency column are always alike will help here.

And then it's just a case of subtracting to complete the frequencies using the cumulative frequency column that we've taken from the coordinates on the graph.

That's all for this lesson.

Thank you for watching.