Interquartile Range: How to Find It
The interquartile range (IQR) measures the spread of the middle half of a data set. It is found by subtracting the first quartile from the third quartile:
IQR = Q3 − Q1
Steps
- Order the data from least to greatest.
- Find Q1: the median of the lower half of the data.
- Find Q3: the median of the upper half of the data.
- Subtract: Q3 − Q1.
If there is an odd number of values, do not include the overall median in either half when finding Q1 and Q3.
How to check your answer
- The IQR should never be negative.
- Since it measures a distance, your answer should be a single number.
- Make sure Q3 is at least as large as Q1.
Common mistakes
- Forgetting to sort the data first.
- Using the overall median instead of the quartiles.
- Including the median in the halves when the data set has an odd number of values.
Quick reminder
The interquartile range tells you how spread out the middle 50% of the data is. Once you find Q1 and Q3 correctly, the final step is just subtraction.