1. What is the Interquartile Range (IQR)?

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). It describes the spread of the middle 50% of data values.

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 provides a robust measure of spread that is less affected by outliers or extreme values than the range.

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) and for constructing box plots. It's a key descriptive statistic for skewed distributions.

4. Using the Calculator

Tips: Enter Q1 and Q3 values (must be numeric). The calculator will compute the difference between these quartiles to give the IQR.

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 the middle 50% of data, making it resistant to outliers.

Q2: How do I find Q1 and Q3?
A: Sort your data and find the median. Q1 is the median of the lower half, Q3 of the upper half (for odd n, exclude the median).

Q3: When should I use IQR instead of standard deviation?
A: Use IQR for skewed distributions or when outliers are present. Use standard deviation for normal distributions.

Q4: What does a large IQR indicate?
A: A large IQR indicates greater variability in the central portion of your dataset.

Q5: Can IQR be negative?
A: No, since Q3 should always be greater than Q1 in proper calculations, IQR is always non-negative.