1. What is the Interquartile Range?

The Interquartile Range (IQR) is a measure of statistical dispersion, representing the range between the first quartile (Q1, 25th percentile) and the third quartile (Q3, 75th percentile). 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 provides a robust measure of spread that is less influenced by outliers than the total range.

3. Importance of IQR Calculation

Details: IQR is crucial for identifying outliers (typically defined as values below Q1-1.5×IQR or above Q3+1.5×IQR), creating box plots, and comparing spread between different data sets.

4. Using the Calculator

Tips: Enter Q3 and Q1 values in the same units. Q3 must be greater than Q1 for a valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: How is IQR different from range?
A: Range considers all data points (max-min) while IQR focuses on the middle 50%, making it resistant to extreme values.

Q2: When should I use IQR instead of standard deviation?
A: Use IQR for skewed distributions or when outliers are present. Use standard deviation for normally distributed data.

Q3: How do I find Q1 and Q3 from raw data?
A: Sort data, find median. Q1 is median of lower half, Q3 is median of upper half (with variations for even/odd n).

Q4: Can IQR be negative?
A: No, since Q3 must be ≥ Q1 by definition, IQR is always ≥ 0.

Q5: What does a large IQR indicate?
A: A large IQR suggests greater variability in the central portion of your dataset.