1. What is the Interquartile Range?

The Interquartile Range (IQR) is a measure of statistical dispersion that represents the range between the first quartile (Q1) and the third quartile (Q3) in a dataset. It's a robust measure of variability that is less affected by outliers than the total range.

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 measures the spread of the middle 50% of data values, providing a clearer picture of data distribution than the full range.

3. Importance of IQR Calculation

Details: IQR is crucial for identifying outliers, understanding data variability, and comparing distributions across different datasets. It's widely used in box plots and descriptive statistics.

4. Using the Calculator

Tips: Enter Q3 and Q1 values in the same units. Both values must be positive numbers, and Q3 must be greater than Q1 for a valid calculation.

5. Frequently Asked Questions (FAQ)

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

Q2: How do you identify outliers using IQR?
A: Outliers are typically defined as values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR.

Q3: When should I use IQR instead of standard deviation?
A: Use IQR when your data has outliers or is not normally distributed, as it's a more robust measure of spread in these cases.

Q4: Can IQR be zero?
A: Yes, if Q3 equals Q1, the IQR is zero, indicating no variability in the middle 50% of the data.

Q5: How is IQR used in box plots?
A: In box plots, the box represents the IQR, with the line inside showing the median, and whiskers extending to non-outlier values.