Interquartile Range Calculator
Statistical Results:
What is Interquartile Range (IQR)?
The Interquartile Range (IQR) is a measure of statistical dispersion that represents the range between the first quartile (Q1) and third quartile (Q3) of a dataset. It contains the middle 50% of the data and is calculated as IQR = Q3 - Q1.
IQR is resistant to outliers and provides a robust measure of spread, making it useful for identifying outliers and understanding data distribution.
How It Works
Enter Data
Input numbers separated by commas
Sort Data
Arrange in ascending order
Find Quartiles
Calculate Q1, Q2, Q3
Formula: IQR = Q3 - Q1
Where Q1 = 25th percentile, Q3 = 75th percentile
Common Examples
Calculation Table
| Dataset | Q1 | Q3 | IQR | Outlier Fences |
|---|---|---|---|---|
| [1,2,3,4,5] | 2 | 4 | 2 | [-1, 7] |
| [10,20,30,40,50] | 20 | 40 | 20 | [-10, 70] |
| [1,3,5,7,9,11] | 3.5 | 8.5 | 5 | [-4, 16] |
| [2,4,6,8,10,12] | 4.5 | 9.5 | 5 | [-3, 17] |
| [1,5,10,15,20] | 5 | 15 | 10 | [-10, 30] |
| [0,1,2,3,4,5,6] | 1.5 | 4.5 | 3 | [-3, 9] |
| [5,10,15,20,25] | 10 | 20 | 10 | [-5, 35] |
| [1,1,2,3,5,8,13] | 1.5 | 6.5 | 5 | [-6, 14] |
Frequently Asked Questions
What is the difference between IQR and range?
Range is the difference between maximum and minimum values (max - min), while IQR is the difference between the third and first quartiles (Q3 - Q1). IQR is more robust against outliers.
How do you identify outliers using IQR?
Outliers are values below Q1 - 1.5×IQR (lower fence) or above Q3 + 1.5×IQR (upper fence). This is known as the 1.5×IQR rule or Tukey's method.
What do Q1, Q2, and Q3 represent?
Q1 (first quartile) is the 25th percentile, Q2 (second quartile) is the median or 50th percentile, and Q3 (third quartile) is the 75th percentile of the dataset.
Why is IQR useful in statistics?
IQR measures the spread of the middle 50% of data, making it resistant to extreme values. It's useful for comparing variability between datasets and creating box plots.
How many data points do I need for IQR?
You need at least 4 data points to calculate meaningful quartiles and IQR. With fewer points, the quartile calculations become less meaningful.
What are real-world applications of IQR?
IQR is used in quality control, data analysis, box plot construction, outlier detection in finance, medical research, and any field requiring robust measures of data spread.