1. What is Interquartile Range?

The Interquartile Range (IQR) is a measure of statistical dispersion, representing the range between the first quartile (25th percentile) and third quartile (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 contains the middle 50% of the data. A larger IQR indicates greater variability in the central portion of the dataset.

3. Importance of IQR

Details: IQR is crucial for identifying outliers (typically defined as values below Q1-1.5×IQR or above Q3+1.5×IQR), comparing variability between datasets, and constructing box plots.

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 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 resistant to outliers.

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

Q3: How is IQR used in box plots?
A: The box in a box plot represents the IQR, with the median marked inside the box and "whiskers" typically extending to 1.5×IQR.

Q4: Can IQR be negative?
A: No, since Q3 is always greater than or equal to Q1, IQR is always non-negative.

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 to non-normal distributions.