The Interquartile Range (IQR) is a measure of statistical dispersion, or how spread out the middle 50% of a dataset is. It is calculated as:

$IQR = Q_3 - Q_1$

where:

• $Q_1$ (first quartile) is the 25th percentile of the data, meaning 25% of the data points are below this value.
• $Q_3$ (third quartile) is the 75th percentile of the data, meaning 75% of the data points are below this value.

What does the IQR represent?

• The IQR represents the range within which the middle 50% of the data lies.
• It is a robust measure of variability, meaning it is resistant to extreme values (outliers), unlike the standard deviation.
• It helps in identifying outliers using the 1.5×IQR rule:
  • Any data point below $Q_1 - 1.5 \times IQR$ or above $Q_3 + 1.5 \times IQR$ is considered an outlier.

Would you like an example or a step-by-step calculation?

Related Questions:

1. How do you calculate the IQR from a given dataset?
2. What is the difference between IQR and standard deviation?
3. How does IQR help in detecting outliers?
4. What are some real-world applications of the IQR?
5. How does IQR change if you add an extreme outlier to the dataset?

Tip:

The IQR is especially useful in boxplots, where it defines the size of the box and helps visualize data spread and potential outliers.