What you’ll learn
Calculate interquartile range.
Key idea
Each quartile is its half's median under the stated convention; IQR is their difference, not the full range.
Keep the stated quartile convention; IQR is upper minus lower quartile, not full range, a quartile alone or their sum.
Worked example
Enter the exact value or ordered values in the format requested below.
Ordered data are (2, 10, 18, 26, 34, 42, 50, 58). Define Q1 and Q3 as medians of the lower four and upper four. Enter exact IQR.
- Using median-of-halves, lower quartile is (10+18)/2=14, upper quartile is (42+50)/2=46.
- The interquartile range is Q3-Q1=46-14=32.
Answer: 32
Quick Check
Evaluate a worked attempt at calculate interquartile range, identify the first invalid step, and provide the correction.
For ordered data (6, 7, 8, 9, 10, 11, 12, 13), a student writes Step 1: Q1=15/2. Step 2: Q3=23/2, using median-of-halves. Step 3: IQR=Q1+Q3=19. Locate the first invalid step and correct it.