IQR Calculator - Interquartile Range
Calculate the interquartile range and quartiles to measure data variability and identify outliers
Enter Your Data Values
Enter numerical values one by one. The calculator supports up to 50 values and requires a minimum of 4 values for calculation.
Enter At Least 4 Values
Please enter at least 4 numerical values to calculate the interquartile range. You currently have 0 valid values.
Example: Test Scores Analysis
Student Test Scores
N = 8 students
IQR Calculation Steps
1. Lower Quartile Rank: LQR = 0.25 × (8 + 1) = 2.25
2. Q1 Calculation: Q1 = 82 + 0.25 × (85 - 82) = 82.75
3. Upper Quartile Rank: UQR = 0.75 × (8 + 1) = 6.75
4. Q3 Calculation: Q3 = 95 + 0.75 × (98 - 95) = 97.25
5. IQR = Q3 - Q1 = 97.25 - 82.75 = 14.5
Interpretation
The middle 50% of students scored within a range of 14.5 points, indicating moderate variability in test performance.
IQR Applications
Quick Tips
IQR contains the middle 50% of your data
Larger IQR indicates more spread in data
IQR is resistant to outliers and skewness
Used in box plots and outlier detection
Understanding Interquartile Range (IQR)
What is IQR?
The Interquartile Range (IQR) is a measure of statistical dispersion that represents the range containing the middle 50% of data values. It's calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
Key Advantages
- •Resistant to outliers and extreme values
- •Works well with skewed distributions
- •Easy to interpret and visualize
- •Essential for box plot construction
IQR Calculation Method
LQR = 0.25 × (N + 1)
UQR = 0.75 × (N + 1)
Q1 = x[LQR] + frac × (x[LQR+1] - x[LQR])
Q3 = x[UQR] + frac × (x[UQR+1] - x[UQR])
IQR = Q3 - Q1
Outlier Detection
Outlier Rules:
• Lower Fence = Q1 - 1.5 × IQR
• Upper Fence = Q3 + 1.5 × IQR
Values outside these fences are potential outliers