Lesson video

Hello, my name's Miss Parnham.

In this lesson, we're going to learn how to find quartiles and interquartile range from a cumulative frequency diagram.

We can use a cumulative frequency diagram to estimate the median and interquartile range.

You may have come across the word median before.

It means the middle value.

So from this diagram, we can see that there are 80 values, because the diagram ends at 80 on the vertical scale.

So the middle value will be about the 40th value.

So we're able to rule a horizontal line from 40, then take a reading from our graph and estimate the median as 13.

2.

The interquartile range is found by finding the difference between the lower quartile and the upper quartile.

Let's find the lower quartile first.

The median, as we've said before, is halfway through the data.

The lower quartile is one-quarter of the way through the data.

So we would rule a line at 20 because 20 is a quarter of 80, the total frequency, and take a reading a very similar way to the median.

So this gives us a lower quartile of nine metres.

So this is a quarter of the way through the data.

The upper quartile is three-quarters of the way through the data.

So this would mean, in this example, ruling a horizontal line from 60, because 60 is three-quarters of 80, or you can think of it as being a quarter less than 80.

So this upper quartile, which is three-quarters of the way through the data, gives us a reading of 17.

4 metres.

The interquartile range is the difference between these two.

It is the range of the middle half because it goes from one-quarter of the way through the data to three-quarters of the way through the data.

So subtracting nine from 17.

4 gives us 8.

4 metres.

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.

Rosie's made quite a common error here.

Often the total frequency is a multiple of 10 and when we put that scale on the vertical axis we often finish on the final value that we need for our last coordinate.

But here because the total is 24, and the scale goes up to 30, Rosie's made that error of just halving the 30 to find the position of the median rather than halving 24.

Here is 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.

Your answers may differ slightly from these because we're reading from a scale and if you're within about 0.

2 of these results for the median and the quartiles, then go ahead and mark those correct, and as long as your estimate for the interquartile range is the difference between your upper and lower quartile results, then you can mark that right as well.

We can interpret further information from a cumulative frequency diagram.

This example asks us to estimate how many ribbon reels contain 12 metres or less.

So on this occasion, we're going to rule a vertical line from a point on the horizontal axis where we have 12 metres and take a reading.

This tells us that there are approximately 32 reels which contain 12 metres or less.

This further question asks us to estimate how many reels have more than 21 metres of ribbon on them.

So just like before, we rule a line from 21 on the horizontal axis, and then take a reading from the vertical axis.

This tells us that 75 reels have 21 metres or less.

But the question asks us for more.

So we need to know to subtract this from the total frequency of 80.

So five reels have more than 21 metres.

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.

If you have 17 or 19 for this question then you can mark those correct.

There's always a margin for error with questions like this because we're reading between intervals on a scale.

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's the answer.

The cumulative frequency diagram show us that 44 people scored 80% or less.

So we need to know to subtract this from the total frequency of 50 to get six.

If you're out by one on this question, then again mark that correct because we are reading from a scale.

That's all for this lesson.

Thank you for watching.