In statistics, the range and interquartile range are two ways to measure the spread of values in a dataset.
The range measures the difference between the minimum value and the maximum value in a dataset.
The interquartile range measures the difference between the first quartile (25th percentile) and third quartile (75th percentile) in a dataset. This represents the spread of the middle 50% of values.
Example: How to Calculate Range & Interquartile Range
Suppose we have the following dataset:
Dataset: 1, 4, 8, 11, 13, 17, 19, 19, 20, 23, 24, 24, 25, 28, 29, 31, 32
We can use the following steps to calculate the range:
- Range = Maximum value – Minimum value
- Range = 32 – 1
- Range = 31
We can use the Interquartile Range Calculator to help us calculate the interquartile range:
- Interquartile Range = 3rd Quartile – 1st Quartile
- Interquartile Range = 26.5 – 12
- Interquartile Range = 14.5
The range tells us the spread of the entire dataset while the interquartile range tells us the spread of the middle half of the dataset.
Range vs. Interquartile Range: Similarities & Differences
The range and interquartile range share the following similarity:
- Both metrics measure the spread of values in a dataset.
However, the range and interquartile range have the following difference:
- The range tells us the difference between the largest and smallest value in the entire dataset.
- The interquartile range tells us the spread of the middle 50% of values in the dataset.
Range vs. Interquartile Range: When to Use Each
We should use the range when we’re interested in understanding the difference between the largest and smallest values in a dataset.
For example, suppose a professor administers an exam to 100 students. She can use the range to understand the difference between the highest score and the lowest score received by all of the students in the class.
Conversely, we should use the interquartile range when we’re interested in understanding the spread between the 75th percentile and 25th percentile of a dataset.
For example, if a professor administers an exam to 100 students, she can use the interquartile range to quickly understand the difference in exam score between a student who scored at the 75th percentile of scores and a student who scored at the 25th percentile.
It’s worth noting that we don’t have to choose between using the range or the interquartile range to describe the spread of values in a dataset.
We can use both metrics since they provide us with completely different information.
The Drawback of Using the Range
The range suffers from one drawback: It is influenced by outliers.
To illustrate this, consider the following dataset:
Dataset: 1, 4, 8, 11, 13, 17, 19, 19, 20, 23, 24, 24, 25, 28, 29, 31, 32
The range of this dataset is 32 – 1 = 31.
However, consider if the dataset had one extreme outlier:
Dataset: 1, 4, 8, 11, 13, 17, 19, 19, 20, 23, 24, 24, 25, 28, 29, 31, 32, 378
The range of this dataset would now be 378 – 1 = 377.
Notice how the range changes dramatically as a result of one outlier.
Before calculating the range of any dataset, it’s a good idea to first check if there are any outliers that could cause the range to be misleading.
Additional Resources
The following tutorials provide additional information about the interquartile range:
How to Interpret Interquartile Range
How to Find Outliers Using the Interquartile Range
How to Calculate the Interquartile Range in Excel
