Quartile Calculator Formula
Understand the math behind the quartile calculator. Each variable explained with a worked example.
Formulas Used
Q1 (25th Percentile)
q1 = (v1 + v2) / 2Q2 (Median)
q2 = v3Q3 (75th Percentile)
q3 = (v4 + v5) / 2IQR (Q3 - Q1)
iqr = (v4 + v5) / 2 - (v1 + v2) / 2Variables
| Variable | Description | Default |
|---|---|---|
v1 | Value 1 (Min) | 10 |
v2 | Value 2 | 20 |
v3 | Value 3 | 30 |
v4 | Value 4 | 40 |
v5 | Value 5 (Max) | 50 |
How It Works
How to Compute Quartiles
Steps (for 5 sorted values)
1. Q2 (Median): The middle value (3rd of 5) 2. Q1: Median of the lower half (values 1 and 2), so Q1 = (v1 + v2) / 2 3. Q3: Median of the upper half (values 4 and 5), so Q3 = (v4 + v5) / 2
Quartiles divide the sorted dataset into four equal parts. Q1 separates the lowest 25%, Q2 is the median, and Q3 separates the lowest 75%.
Worked Example
Find the quartiles of the sorted dataset: 10, 20, 30, 40, 50.
- 01Q2 (Median) = v3 = 30
- 02Lower half: 10, 20 → Q1 = (10 + 20) / 2 = 15
- 03Upper half: 40, 50 → Q3 = (40 + 50) / 2 = 45
- 04IQR = 45 - 15 = 30
Frequently Asked Questions
What do quartiles represent?
Q1 is the value below which 25% of data falls, Q2 (the median) below which 50% falls, and Q3 below which 75% falls. They divide the sorted data into four equal-sized groups.
Are there different methods to compute quartiles?
Yes. Different software uses different interpolation methods (e.g., inclusive vs. exclusive). The results can differ slightly depending on the method, especially for small datasets.
How do quartiles relate to percentiles?
Q1 is the 25th percentile, Q2 is the 50th percentile, and Q3 is the 75th percentile. Quartiles are specific percentile landmarks.
Learn More
Guide
How to Calculate Percentiles and Quartiles
Learn how to calculate percentiles and quartiles from a dataset. This guide explains the percentile rank formula, the interquartile range, and how these measures describe data distribution.
Ready to run the numbers?
Open Quartile Calculator