1. What is the Interquartile Range?

The Interquartile Range (IQR) is a measure of statistical dispersion that represents the range between the first quartile (Q1) and the third quartile (Q3). It describes the middle 50% of values when ordered from lowest to highest.

2. How Does the Calculator Work?

The calculator uses the simple IQR formula:

Where:

• \( Q3 \) — Third quartile (75th percentile)
• \( Q1 \) — First quartile (25th percentile)

Explanation: The IQR is resistant to outliers and gives a better sense of the data's spread than the full range.

3. Importance of IQR Calculation

Details: IQR is crucial for identifying outliers (commonly defined as values below Q1-1.5×IQR or above Q3+1.5×IQR) and for constructing box plots. It's a robust measure of variability.

4. Using the Calculator

Tips: Enter Q3 and Q1 values (must be in the same units). Q3 should be greater than Q1 for meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: How is IQR different from range?
A: Range considers only the extremes (max-min), while IQR focuses on the middle 50% of data, making it less sensitive to outliers.

Q2: What does a large IQR indicate?
A: A large IQR suggests greater variability in the central portion of your dataset.

Q3: Can IQR be negative?
A: No, since Q3 must be greater than Q1 by definition, IQR is always non-negative.

Q4: How do I find Q1 and Q3?
A: Sort your data, then Q1 is the median of the first half and Q3 is the median of the second half.

Q5: When should I use IQR instead of standard deviation?
A: Use IQR when your data has outliers or isn't normally distributed, as it's more robust.