1. What is Interquartile Range?

The interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the middle 50% of data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

2. How Does the Calculator Work?

The calculator uses the IQR formula:

Where:

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

Explanation: The IQR represents the range of the middle 50% of the data, making it a robust measure of spread that is less affected by outliers than the range.

3. Importance of IQR Calculation

Details: IQR is crucial for identifying variability in data, detecting outliers (often defined as values below Q1-1.5×IQR or above Q3+1.5×IQR), and comparing distributions.

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: Why use IQR instead of range?
A: IQR is more resistant to outliers since it only considers the middle 50% of data, while range uses the extreme values.

Q2: How do I find Q1 and Q3?
A: Sort your data, find the median, then Q1 is the median of the lower half and Q3 is the median of the upper half.

Q3: When should I use IQR?
A: Use IQR when your data has outliers or is skewed. For symmetric, normal distributions, standard deviation may be more appropriate.

Q4: What does a large IQR indicate?
A: A large IQR indicates greater variability in the central portion of your dataset.

Q5: Can IQR be negative?
A: No, since Q3 is always greater than Q1 in properly calculated quartiles, IQR is always positive.