Lesson video

Hello, my name's Miss Parnham.

In this lesson, we're going to learn how to find quartiles from a list of data.

You may have come across the words, median, upper and lower quartiles and interquartile range in the context of cumulative frequency diagrams. But before we tackle this example, I will go through the definitions for each.

So you understand what we're trying to find today.

The median is the middle value of a dataset once they've been ordered.

It's halfway through the data.

The lower quartile is a quarter of the way through the data, once they've been ordered.

And the upper quartile is three quarters of the way through the data.

Again, once they've been ordered.

And the way to calculate the interquartile range is to find the difference between the upper and lower quartiles.

Let's now look at this example.

I must start by putting them in order.

We find the median by identifying the middle value.

So in this example, the median is 20.

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

The best way to look at this is to look at all the numbers before the media and find the middle value.

This is the lower quartile.

So the lower quartile is 17.

And then almost in exactly the same way, the upper quartile is the middle number of the numbers that follow the median.

So here we have 24.

So the upper quartile is 24.

See how evenly they are spaced.

Two numbers and then the lower quartile, two numbers and then the median, two numbers and then the upper quartile and finally two numbers.

To work out the interquartile range, we simply need to do 24 subtract 17, which is seven.

And this is the range of the middle half of the data.

Here's some questions for you to try.

Pause the video to complete the task.

And restart the video when you're finished.

Here are the answers.

The first dataset was ordered already.

So you just needed to find the median, the lower and upper quartiles before finding the interquartile range.

Whereas the subsequent datasets, needed you to order them first.

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.

The quartiles are the midpoints between the second and third, and the seventh and eighth values.

And when we need to find the value in between two numbers, then we need to add them together and divide by two, if they're not the same value.

Let's look at a further example where we find the median, upper and lower quartiles and intequartile range for a set of data.

This time, we have an even number of values in the dataset, and that changes things slightly.

Let's start by doing exactly the same and putting them in ascending order.

The median is the middle value but because we have an even number of values in the dataset, there's one number in the middle.

So we're looking for the midpoint of 19 and 20.

Because they're not the same number, we have to add them together and divide by two to get the answer 19.

5.

So the median is 19.

5, not 19 or 20.

So let's think about the six numbers before the median and find the middle of them.

Again, this is a gap between two numbers.

So we add together 17 and 18 and divide by two in order to find the lower quartile.

This is 17.

5.

Then think about the six numbers, which follow the median.

I'm finding the middle of them.

Here we have the middle of 23 and 24.

So we add them together and half it and that gives us the upper quartile of 23.

5.

So the interquartile range is the difference between our two quartiles.

And this is six.

Here's some questions for you to try.

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

Here are the answers.

Only the first data set has been ordered already.

So the subsequent parts of B and C need to be put in order before you find the median and the lower and upper quartiles.

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.

Because this cards has been ordered, we can see the median is 8.

5, in the middle of eight and nine.

So doubling that for the range gets to 17.

And then if the range is 17 and we know the lowest is two, adding 17 on to two, gives us 19 for card marked with the letter a.

And then we can see that the lower quartile between four and five is 4.

5.

The interquartile range is six.

So adding six onto that gives us 10.

5 and 10.

5 is in the middle of nine and 12.

And we can work that out by doubling the 10.

5 to get 21 and subtracting 12.

And that's how we know that b is nine.

That's all for this lesson.

Thank you for watching.