What Are the Benefits of Using Interquartile Range Instead of Range?

When we look at how to understand data in statistics, we often compare two ways: the range and the interquartile range (IQR). Both of these help us see how spread out our data is, but they have some differences.

The Range is the simplest way to find out how spread out the data is. It shows the gap between the highest and lowest values.

However, it has some problems:

1. Sensitive to Outliers:

   • The range can be greatly affected by outliers. Outliers are extreme numbers that stand out from the rest. For example, if we have test scores like 50, 55, 60, 65, and 100, the range would be $100 - 50 = 50$. This number suggests there's a big difference in scores, but that's not true for most of the students.
   • What to Do: You could find and remove the outliers, but that could cause other issues.

2. Lacks Detail:

   • The range only gives a simple picture of the data spread. It doesn’t tell us how the other numbers are arranged. For example, we can't tell if most scores are close together or far apart based solely on the range.
   • What to Do: By using quartiles, we can see a better picture of how the data is spread out, as it splits the data into four equal parts.

On the other hand, the Interquartile Range (IQR) focuses on the middle 50% of the data. It looks at the first quartile (Q1) and third quartile (Q3) and is found by this formula:

$\text{IQR} = Q3 - Q1$

Here’s why the IQR can be better:

1. More Stable Against Outliers:

   • The IQR ignores the lowest 25% and the highest 25% of the data. This makes it more reliable because it gives a clear view of where most numbers are and doesn’t let a few extreme values change the result too much.

2. Better Focus on Data Clustering:

   • The IQR shows how numbers are grouped around the middle. A small IQR means the numbers are similar, while a big IQR shows a lot of variety in the middle 50% of the data.

In conclusion, the IQR does a great job of reducing the impact of outliers and helps us see how data is grouped compared to the range. However, it can be a little tricky, as it requires more steps to calculate and might be hard to understand for someone not familiar with quartiles.