Interquartile Range (IQR)

Introduction: IQR

The Interquartile Range (IQR) is a statistical measure that describes the spread of the middle 50% of a dataset. By focusing on the central portion of the data, the IQR provides a clear view of variability without being overly influenced by extreme values or outliers.

Background

Data dispersion measures such as range and standard deviation are often distorted by unusually high or low values. The IQR solves this issue by using quartiles, making it a robust tool for analysing datasets where outliers are present. It is commonly used in descriptive statistics, quality control, and data analysis.

Key Elements/Features

• Quartiles:
  • Q1 (First Quartile): Median of the lower half of the dataset.
  • Q2 (Median): Divides the dataset into two equal halves.
  • Q3 (Third Quartile): Median of the upper half of the dataset.

Formula: IQR = Q3 − Q1

This represents the range of the middle 50% of values.

• Boxplot Representation: The IQR is shown as the “box” in a boxplot, with whiskers extending up to 1.5 × IQR from Q1 and Q3 to highlight most data points.
• Robustness: Less sensitive to outliers compared to range or standard deviation.

Applications/Examples

• Economics: Analysing income distributions while minimising the effect of extreme wealth.
• Engineering: Measuring process variation in quality control.
• Social Sciences: Studying survey results where a few extreme answers may otherwise distort findings.
• Education: Comparing exam score distributions among student groups.

Relevance/Impact

The IQR is vital for understanding variability in datasets, especially when outliers could mislead conclusions. By focusing on the central spread, it allows analysts and decision-makers to work with reliable insights.

See also

• Boxplot
• Median
• Standard Deviation
• Range