AI agents can use /llms.txt as a documentation index. Follow listed markdown links; .md URLs and Accept: text/markdown work only for supported source-backed pages.
We already know how to find the mean of data. But sometimes, the mean alone isn't enough to describe the data. Imagine two groups of friends with the same average age, but when you look closer, the age spread within each group is very different.
This is where the Interquartile Range () comes in handy! The is a measure of data spread that focuses on the middle of the data after it has been sorted.
Why focus on the middle? Sometimes data has values at the extremes (too small or too large, called outliers) that can make other spread measures (like the Range) less accurate. The is more "resistant" to these extreme values.
The formula is super simple:
So, the is the difference between the upper and lower quartiles.
To make it clearer, let's look at an example.
There are two groups, each with . Let's look at their age data in the table below:
| Data Point # | Group One | Group Two |
|---|---|---|
Let's calculate some statistics for these two groups.
Mean (Average):
If you calculate the average age for both groups, the result is exactly the same, old.
Group :
Group :
Quartiles ( and ):
After sorting the data (as in the table above), we find the positions of the quartiles.
Group One (): The position of is at data point . This means is between the () and () data points. Since both values are the same, then
Now let's calculate the measures of spread.
Range:
Range Group One is
Range Group Two is
Wow, the ranges are very different! Group Two's data is much more spread out when looking at the extreme values.
Interquartile Range ():
Let's summarize in a table for easy comparison:
| Group | Mean | Range | Interquartile Range () | ||
|---|---|---|---|---|---|
| One |
Even if the average is the same, the spread of the data can be very different. The helps us see how spread out the middle part of the data is, giving a better picture of data variation than just looking at the mean or range, especially when there are extreme values.
The position of is at data point . This means is between the () and () data points. Since both values are the same, then
Group Two (): The position of is at data point . This means is between the () and () data points. In this case, we can take the average of these two data points:
The position of is at data point . This means is between the () and () data points. Similarly, we take their average:
Group One is
Group Two is
The values are also very different!
| Two |
