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 spread of the middle 50% of data values.

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 affected by outliers or extreme values than the total range.

3. Importance of IQR

Details: The IQR is used to identify outliers (often defined as values below Q1-1.5×IQR or above Q3+1.5×IQR), compare variability between datasets, and create box plots. It's particularly useful for skewed distributions.

4. Using the Calculator

Tips: Enter Q3 and Q1 values in the same units. Q3 must be greater than Q1. The result will be in the same units as your input values.

5. Frequently Asked Questions (FAQ)

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

Q2: When should I use IQR instead of standard deviation?
A: Use IQR for skewed distributions or when outliers are present. Standard deviation is better for symmetric, normal distributions.

Q3: How do I find Q1 and Q3 from raw data?
A: Sort your data, then Q1 is the median of the first half and Q3 is the median of the second half (with special handling for odd numbers).

Q4: Can IQR be negative?
A: No, since Q3 must be greater than Q1 by definition, IQR is always non-negative.

Q5: What does a large IQR indicate?
A: A large IQR indicates greater variability in the middle 50% of your data values.