1. What is 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) of 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 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 Calculation

Details: IQR is crucial for identifying outliers (commonly 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. The calculator will compute the difference between these two values 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 related to box plots?
A: In box plots, the box represents the IQR, with the line inside showing the median. Whiskers typically extend to 1.5×IQR from the quartiles.

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

Q4: What's the difference between IQR and standard deviation?
A: IQR measures spread based on quartiles, while standard deviation measures spread based on mean. IQR is more robust to outliers.

Q5: How do I find quartiles from raw data?
A: Sort the data, find the median to split into two halves. Q1 is the median of the lower half, Q3 of the upper half.