Interquartile Range (IQR) – A Robust Measure of Spread

Posted on by uplatzblog

🔹 Short Description:
 IQR measures the spread of the middle 50% of data, helping identify variability while minimizing the influence of outliers. It’s a key tool in box plots and exploratory data analysis.

🔹 Description (Plain Text):

The Interquartile Range (IQR) is a measure of statistical dispersion that captures the range within which the central 50% of a dataset lies. It is particularly useful because it ignores extreme values and focuses on the “middle bulk” of the data, making it a robust indicator of variability.

Formula:
 IQR = Q3 − Q1

Where:

  • Q1 (First Quartile) is the 25th percentile (the value below which 25% of data fall) 
  • Q3 (Third Quartile) is the 75th percentile (the value below which 75% of data fall) 

Example:
 Consider the dataset: 2, 4, 6, 8, 10, 12, 14, 16, 18

  • Q1 = 6 
  • Q3 = 14 
  • IQR = 14 − 6 = 8 

This means the middle 50% of the data is spread across 8 units.

Why IQR Is Important:
 Unlike the range, which uses only the minimum and maximum values, the IQR focuses on the center of the data. This makes it resistant to outliers and more reliable for datasets with extreme values.

Real-World Applications:

  • Education: Evaluating consistency in exam results 
  • Finance: Assessing interquartile earnings or price dispersion 
  • Data Science: Detecting outliers using the 1.5 × IQR rule 
  • Healthcare: Analyzing median response time or treatment results 
  • Box Plots: IQR is used to define the height of the box and whisker boundaries 

Key Insights:

  • The IQR gives a clearer picture of variability by focusing on the central portion of the data 
  • In a box plot, data points that fall below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are considered outliers 
  • A small IQR indicates data is tightly packed around the median 
  • A large IQR shows greater spread in the central data values 

Limitations:

  • While IQR is great for spotting spread, it doesn’t provide exact values of min or max 
  • It assumes a ranked dataset and may require sorting and interpolation in complex datasets 

By using IQR, you get a reliable sense of how your data behaves in the middle — without being misled by outliers or extreme values.

🔹 Meta Title:
 Interquartile Range (IQR) – Formula, Use Cases, and Outlier Detection

🔹 Meta Description:
 Explore the Interquartile Range (IQR), a robust statistical tool that captures the middle 50% of your data. Learn how to calculate Q1 and Q3, detect outliers, and apply IQR in box plots, finance, and education for meaningful data insights.