An interquartile range calculator identifies the spread of the middle 50% of values in a dataset.
How to calculate the interquartile range:
The IQR measures statistical dispersion by capturing the range between the first and third quartiles, making it resistant to outliers.
Step-by-step method:
- List all values in the dataset
- Sort the values in ascending order
- Find the median — this splits the dataset into a lower half and an upper half
- Find Q1 — the median of the lower half
- Find Q3 — the median of the upper half
- Subtract: IQR = Q3 − Q1
Formula:
IQR = Q3 − Q1
Where Q1 is the 25th percentile and Q3 is the 75th percentile of the dataset.
Examples
Example 1: Dataset {1, 3, 5, 7, 9}
- Sorted: 1, 3, 5, 7, 9
- Median = 5 → lower half = {1, 3}, upper half = {7, 9}
- Q1 = (1+3) / 2 = 2, Q3 = (7+9) / 2 = 8
- IQR = 8 − 2 = 6.0000
Example 2: Dataset {2, 4, 4, 5, 6, 7, 8, 9}
- Sorted: 2, 4, 4, 5, 6, 7, 8, 9
- Median = (5+6) / 2 = 5.5 → lower half = {2, 4, 4, 5}, upper half = {6, 7, 8, 9}
- Q1 = (4+4) / 2 = 4, Q3 = (7+8) / 2 = 7.5
- IQR = 7.5 − 4 = 3.5000
Key features include:
- Input for up to 50 values
- Automatic calculation
- Displays Q1, Median, Q3, and IQR together
- Flexible list management — add or remove values freely
- Support for decimals and negative numbers
- Dynamic recalculation on every change