Quartile Calculator
Find Q1, Q2, Q3, IQR, median, min, max, and range instantly from any dataset.
Accepts commas, spaces, new lines, or mixed delimiters.
Quartile Statistics
| Statistic | Value |
|---|---|
| First Quartile (Q1) | |
| Second Quartile / Median (Q2) | |
| Third Quartile (Q3) | |
| Interquartile Range (IQR) | |
| Minimum | |
| Maximum | |
| Range | |
| Count (n) |
Quartile Reference Table
Each quartile represents a specific percentile of a ranked dataset. Use the table below as a quick reference.
| Quartile | Symbol | Percentile | What It Represents |
|---|---|---|---|
| First Quartile | Q1 | 25th | Median of the lower half of data |
| Second Quartile | Q2 | 50th | Median of the entire dataset |
| Third Quartile | Q3 | 75th | Median of the upper half of data |
| Interquartile Range | IQR | Q3 minus Q1 | Spread of the middle 50% of data |
What Are Quartiles?
Quartiles are values that divide a ranked dataset into four equal groups of 25 percent each. They are essential tools in descriptive statistics for understanding how data is distributed and identifying outliers.
- Q1 (First Quartile) marks the 25th percentile. Twenty-five percent of values fall below Q1.
- Q2 (Second Quartile) is the median, or 50th percentile. Half of all values fall below Q2.
- Q3 (Third Quartile) marks the 75th percentile. Seventy-five percent of values fall below Q3.
Quartiles are widely used in box plots, outlier detection, standardized test scoring, and financial analysis.
How to Calculate Quartiles Step by Step
- Sort your data from the lowest to the highest value.
- Find the median of the full dataset. This is Q2.
- Split the ordered list into a lower half and an upper half at Q2. If the dataset has an odd number of values, exclude Q2 from both halves.
- Find the median of the lower half. This is Q1.
- Find the median of the upper half. This is Q3.
Odd vs Even Dataset Size
When a dataset contains an odd number of values, the middle value becomes Q2 and is excluded from both halves before computing Q1 and Q3. When a dataset contains an even number of values, Q2 is the average of the two central values, and the dataset splits evenly into two halves.
How to Find the Interquartile Range
The interquartile range (IQR) measures the spread of the middle fifty percent of a dataset. IQR is calculated by subtracting Q1 from Q3.
Formula: IQR = Q3 minus Q1
Because the IQR only considers the middle half of data, it is resistant to outliers. This makes it a more robust measure of spread than the simple range when extreme values are present. The IQR is commonly used to build box and whisker plots and to identify outlier boundaries (values below Q1 minus 1.5 times IQR or above Q3 plus 1.5 times IQR are typically flagged as outliers).
Range vs Interquartile Range
The overall range equals the maximum value minus the minimum value. It captures the full spread of data but is sensitive to extreme outliers. The IQR, covering only the central 50 percent, provides a more stable measure of variability in skewed distributions.
Accepted Data Formats
This quartile calculator accepts data in multiple formats so you can paste directly from spreadsheets or text files.
| Format | Example Input | Processed As |
|---|---|---|
| Comma separated | 10, 20, 30, 40 | 10, 20, 30, 40 |
| Space separated | 10 20 30 40 | 10, 20, 30, 40 |
| New lines (column) | 10 20 30 | 10, 20, 30 |
| Mixed delimiters | 10, 20 30,,40 | 10, 20, 30, 40 |