Quartiles calculator
Compute Q1, Q2, Q3, and the interquartile range from up to 12 values using linear interpolation.
What this calculator covers
Use this calculator when the middle-half spread matters more than the full minimum-to-maximum range.
Quartiles are especially useful for skewed lists because the interquartile range focuses on the middle 50% instead of being dominated by the outermost values.
Frequently asked questions
- What are Q1, Q2, and Q3?
- Q1 (the first quartile) is the value below which 25% of the data falls. Q2 is the median, the midpoint of the sorted dataset. Q3 is the value below which 75% of the data falls. Together they divide an ordered dataset into four roughly equal-sized groups.
- How is the interquartile range useful?
- The interquartile range (IQR = Q3 − Q1) measures the spread of the middle half of a dataset. Because it ignores the lowest and highest quarters, it is not pulled by extreme values the way the full range is, making it a more reliable measure of typical spread for skewed distributions.
- Why might the same dataset produce different quartile values in different tools?
- Several quartile calculation methods exist, and different software tools may use different ones. This calculator uses inclusive linear interpolation at the 25th, 50th, and 75th percentiles. If you compare results with a spreadsheet program or statistics package, small differences may appear depending on which method that tool defaults to.
- How many values do I need to enter?
- At least two numeric values are required. Blank fields are ignored, so you can leave unused rows empty without affecting the result.
Tool
Run the calculation
Result
RESULT · IQR
â„–159
Primary result
6
For the sorted values 8, 12, 12, 15, 19, 21, Q1 is 12, Q2 is 13.5, Q3 is 18, and the interquartile range is 6.
- Values used
- 8, 12, 12, 15, 19, 21
- Q1 / Q2 / Q3
- 12 / 13.5 / 18
- Minimum / maximum
- 8 / 21
- Interquartile range
- 6
Step-by-step solution
- 1.Ignore blank fields and sort the numeric values from smallest to largest.
- 2.Use the linear-interpolation percentile rule at 25%, 50%, and 75% to get Q1 12, Q2 13.5, and Q3 18.
- 3.Subtract Q1 from Q3 to get the interquartile range 6, which covers the middle 50% of the data.
Walkthrough
Visual walkthrough
Quartiles divide the ordered data into four equal-probability bands and use the middle half to describe spread more robustly than the full range.
01
Order the dataset
8, 12, 12, 15, 19, 21
Quartiles are defined from the sorted positions, so ordering comes before interpolation.
02
Read Q1, Q2, and Q3
Q1 12 · Q2 13.5 · Q3 18
Linear interpolation fills in percentile positions that land between two observed values.
03
Measure the middle-half spread
The interquartile range trims away the lower and upper quarters and measures only the middle 50% band.
18 - 12 = 6