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) in a data set. It provides a robust measure of spread that is less affected by outliers than the total range.

2. How Does the Calculator Work?

The calculator uses the simple IQR formula:

Where:

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

Explanation: The IQR contains the middle 50% of the data, providing a clear view of the data's central spread while excluding extreme values.

3. Importance of IQR Calculation

Details: The IQR is essential for identifying outliers (commonly defined as values below Q1-1.5×IQR or above Q3+1.5×IQR), comparing distributions, and creating box plots. It's more robust than range as it's not affected by extreme values.

4. Using the Calculator

Tips: Enter the Q1 and Q3 values (which can be calculated from percentile functions or box plots). The calculator will compute the difference between these two values.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between range and IQR?
A: Range uses the minimum and maximum values, while IQR uses Q1 and Q3, making it resistant to outliers.

Q2: How is IQR used in box plots?
A: The box in a box plot represents the IQR, with the line inside showing the median (Q2).

Q3: 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 a more robust measure of spread.

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

Q5: How do I find Q1 and Q3 to use this calculator?
A: Q1 is the median of the first half of data, Q3 of the second half. Many statistical packages have functions to calculate these quartiles.