Interquartile Range Calculator

Quickly find the Interquartile Range (IQR) of your data set. This tool calculates the first quartile (Q1), third quartile (Q3), and the IQR to help you understand the spread of your data, especially for statistics homework or analysis.

Data Set

Enter numbers separated by commas or spaces (e.g., 1, 5, 8, 12, 15)

How it works

Quickly find the Interquartile Range (IQR) of your data set. This tool calculates the first quartile (Q1), third quartile (Q3), and the IQR to help you understand the spread of your data, especially for statistics homework or analysis.

The Formula

1. Sort your data set in ascending order. 2. Calculate Q1 (First Quartile): This is the median of the lower half of the data. 3. Calculate Q3 (Third Quartile): This is the median of the upper half of the data. 4. Interquartile Range (IQR) = Q3 - Q1

Worked Example

Example: Find the IQR for a data set
Let's find the IQR for the data set: 1, 3, 5, 7, 9, 11, 13, 15. 1. Sorted data: 1, 3, 5, 7, 9, 11, 13, 15 (n=8) 2. Q1 (25th percentile): Using the standard method, Q1 is 4.5. 3. Q3 (75th percentile): Using the standard method, Q3 is 11.5. 4. IQR = Q3 - Q1 = 11.5 - 4.5 = 7. This means the middle 50% of the data spans a range of 7.

Tips, Assumptions & Limitations

Enter numbers separated by commas, spaces, or new lines.
The calculator automatically sorts your data for you.
IQR is a robust measure of spread, less affected by outliers than the full range.

FAQ

The Interquartile Range (IQR) is a measure of statistical dispersion, or how spread out your data is. It represents the range of the middle 50% of your data, calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

To calculate Q1 (first quartile), you first sort your data set in ascending order. Q1 is the median of the lower half of the data. Similarly, Q3 (third quartile) is the median of the upper half of the data. Our calculator uses a standard interpolation method to find these values accurately.

The IQR is often preferred over the full range (maximum value - minimum value) because it is less affected by outliers. Since it focuses on the middle 50% of the data, extreme values at either end do not skew the measure of spread, giving a more robust understanding of the central variability.

While you can technically calculate IQR for small data sets, it becomes more meaningful with at least 4 or more data points. For very small sets, the quartiles might not represent a clear 'middle 50%' effectively.