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 third quartile (Q3, 75th percentile) of a dataset. It's a robust measure of variability that's less affected by outliers than the range.

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 represents the middle 50% of the data, providing a measure of spread that's resistant to extreme values.

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), comparing distributions, and understanding data variability in a robust way.

4. Using the Calculator

Tips: Enter Q3 and Q1 values in the same units as your original data. The calculator will compute the difference between these two quartiles to give the IQR.

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, making it a more reliable measure of spread for skewed distributions.

Q2: How is IQR used in box plots?
A: In box plots, the box represents the IQR (from Q1 to Q3), with the median marked inside, and whiskers typically extending to 1.5×IQR from the quartiles.

Q3: What does a large IQR indicate?
A: A large IQR indicates greater variability in the central portion of the dataset, while a small IQR shows data points are clustered closely around the median.

Q4: Can IQR be negative?
A: No, since Q3 is always greater than or equal to Q1, IQR is always non-negative. A zero IQR suggests no variability in the middle 50% of data.

Q5: How is IQR related to standard deviation?
A: For normally distributed data, IQR ≈ 1.35×σ. Both measure spread but IQR is more robust while standard deviation is more sensitive to all data points.