How to Use the Interquartile Range Calculator
This calculator helps you find the interquartile range (IQR) of a dataset and learn how to compute it manually through a step-by-step solution. To use the calculator:
- Enter your data values in the data input field. You can separate values using commas, spaces, tabs, or line breaks. Alternatively, you can copy-paste values directly from Excel, Google Sheets, and text documents.
- Click Calculate.
The calculator will instantly return the IQR and show you exactly how the value was obtained using your own data.
What Is Interquartile Range?
The interquartile range (IQR) is a statistical measure of dispersion that describes the spread of the middle 50% of a data set. To find the IQR, you subtract the lower quartile (Q1) from the upper quartile (Q3).
Therefore, if the IQR is small, it means that the middle half of the data values are close together. However, if the IQR is large, it suggests that the middle half of the data values are more spread out.
The IQR is useful because it focuses on the middle part of the data. Unlike the range, which is highly affected by outliers, IQR is less affected by very small or very large values.
Interquartile Range Formula
The interquartile range formula is: IQR = Q3 − Q1
Where:
- Q1 is the lower quartile.
- Q3 is the upper quartile.
- IQR is the distance between Q1 and Q3.
This calculator focuses on calculating the IQR, assuming that you already know how to compute the first quartile (Q1) and third quartile (Q3). However, if you’re not sure about how to find Q1 and Q3 manually, you may find the quartile calculator useful.
How to Find the Interquartile Range
To find the interquartile range manually:
- Find the lower quartile, Q1.
- Find the upper quartile, Q3.
- Apply the interquartile range formula
Example
Find the interquartile range for the dataset: 8, 10, 12, 14, 18, 20, 22, 24
Solution
To find the interquartile range for the dataset by hand, follow these steps:
Step 1: Find the first quartile (Q1)
The first quartile is the median of the lower half of the data, after it has been arranged in ascending order. Using the quartile calculator, Q1 = 11
Step 2: Find the third quartile (Q3)
The third quartile is the median of the upper half of the data, after it has been arranged from the smallest to the largest. Using the calculator, the third quartile, Q3 = 21
Step 3: Apply the interquartile range formula
By definition, the interquartile range formula is: IQR = Q3 − Q1
Substituting the values into the formula, we have:
IQR = 21 – 11
= 10
Want to verify this result using the IQR calculator? Follow these steps:
- Copy and paste the dataset into the data input field
- Click calculate
The calculator will yield similar results as above and show you how the value was obtained.
Therefore, IQR = 10. This means that the middle 50% of the dataset spreads over 10 units.
IQR vs Range
The range and interquartile range are both measures of spread, but they describe different parts of a dataset. While the range is calculated by subtracting the minimum value from the maximum value, the interquartile range is found by subtracting the first quartile from the third quartile.
This means that the range tells us about the full spread of the dataset, whereas the interquartile range describes the spread of the middle 50% of the dataset.
Unlike the range, which is strongly affected by outliers, the IQR is more resistant to outliers and extreme values because it focuses only on the middle half of the data.
When to Use the Interquartile Range?
Use the interquartile range when you want to measure the spread of the middle part of a dataset. It is especially useful when:
- your data contains outliers,
- the range feels too affected by extreme values,
- you want to describe the spread of the middle 50%,
- you are comparing variability between datasets,
- or you need IQR for a box plot or outlier rule.
Interquartile Range and Outliers
The interquartile range is also used in outlier detection. In particular, it is used to compute the lower fence and upper fence of a dataset using the formulas:
- Lower fence = Q1 − 1.5 × IQR
- Upper fence = Q3 + 1.5 × IQR
In this case, values below the lower fence or above the upper fence are considered to be potential outliers. Want to quickly compute the lower and upper fence for your data and determine whether your data has outliers? Use the lower and upper fence calculator.
Frequently Asked Questions
It calculates the interquartile range (IQR) of a dataset and shows the step-by-step solution.
The interquartile range is the spread of the middle 50% of a dataset. You can simply find it by subtracting the lower quartile (Q1) from the upper quartile (Q3).
The formula is: IQR = Q3 − Q1, where Q1 is the lower quartile, and Q3 is the upper quartile.
IQR is less affected by outliers than the range because it does not use the smallest and largest values directly.
Yes. IQR can be zero when Q1 and Q3 are the same value. This can happen when many values in the middle part of the dataset are equal.
Yes. IQR is commonly used in the 1.5 × IQR rule for detecting potential outliers.
