Find the Estimate of the Median for Grouped Data

When you are given grouped data, how can you find the median class?

 

 

Let's have a look at an example:

 

 

To find the median class, we first need to find which position the median occupies.

 

We can see that we have 8 + 13 + 9 + 5 = 35 data points altogether.

So the median will be on the (35 + 1) ÷ 2 = 18th position.

 

Looking back at our table, we can see that:

- the first 8 numbers, i.e. 1st to 8th, are between 14 m and 18 m

- the next 13 numbers, i.e. 9th to 21st, are between 18 m and 22 m
 

The 18th number is between the 9th and the 21st, so the 18 ≤ m < 22 is the median class.

 

But this is just the class the median is in! 

 

Could we find the actual median?

Well, we can't find the actual median because we don't know what the numbers actually are when we have grouped data like this - but we can find the estimate!

 

We know that the median here is at the 18th position and the 9th to 21st numbers are in the 18 ≤ m < 22 class.

This means that the median is the 10th number within these 13 numbers in the 18 ≤ m < 22 class.

 

The 18 ≤ m < 22 class occupies the 'distance' of 22 - 18 = 4

 

Since there are 13 numbers over this distance, then each number occupies the distance of:

4 ÷ 13 = 0.3076923077 = 0.308 to 3 s.f.

 

So, since the median is the 10th number within these 13, it will be the distance of 10 x 0.308 = 3.08 to the right from 18.

 

So the estimate of the median is 18 + 3.08 = 21.08 to 2 d.p.!

 

 

Don't worry if this seems tricky - remember that you can look back at this introduction at any point by clicking on the red help button on the screen.

 

Grab your calculator and let's have a go at some questions!