How to Work out Interquartile Range: Summary

Here’s a reminder of the key points you should know about the interquartile range.

There are a few different types of measure of spread.

One of those is the range, which we find if we take the largest value in a dataset and subtract the smallest value.

However, if the dataset has extreme values, the range can be misleading.

So to avoid this problem, we can turn to measures of location, called quartiles.

The middlemost value of a data set is called the second quartile.

The value that’s a quarter of the way through is called the first quartile.

And the value that’s three quarters of the way through is called the third quartile.

And we can represent quartiles like this.

These enable us to create a new measure of spread, called the interquartile range [fit in knowledge structure]

…Which is the distance the first quartile and the third quartile. 

And it spans the middle fifty percent of a data set.

Now, splitting datasets into quarters is harder than it might first appear and depends on the number of data points.

As a result, you’ll find different people use different methods, and they can be a bit messy.

We recommend using this formula to find the position of any quartile.

Where q represents the number of the quartile, and n represents the total number of data points.

Now, the position of a quartile must always be a multiple of 0.5.

But occasionally, …

using this formula might get you a result like this or this

If you’re looking for a first quartile and get one of these, always round up to the nearest point five.

And if you’re looking for a third quartile and get one of these, always round down to the nearest point five.

We can also find the value of a quartile.

If the quartile’s position is halfway between two data points, its value is given by the average of the data points on either side.

Finally, when the data set is shown in a frequency table, we can find the value of a quartile by first finding its position.

Then, the cumulative frequency counts.

And lastly, locating the value of a data point at that position.

And when the dataset is shown in a grouped frequency table, we can estimate the value of a quartile using linear interpolation.