The Resistant Measures: Median and IQR

A statistical measure is considered resistant if it is not significantly affected by extreme values (outliers). * Median: Resistant to outliers because it depends only on the physical position of the middle values, not their actual size. * Interquartile Range (IQR): Resistant to outliers because it measures the spread of the middle 50% of the data, completely ignoring the extremes on the ends..

Example: Adding a High Outlier: Consider the data set: 10, 12, 14, 15, 18. The median is 14 and the IQR is 5.5. If we add an extreme outlier of 100 to the end, the new median shifts only slightly to 14.5, and the new IQR is 6. Despite the massive outlier, the median an

Removing a Low Outlier: Consider a data set with a low outlier: 5, 40, 42, 44, 45, 47, 49. The median is 44 and the IQR is 7. If we remove the outlier 5, the new median becomes 44.5 and the new IQR is 5. The values remain relatively stable.

The median acts as a sturdy anchor; it often stays put, completely ignoring the unusual data point. Because it only cares about which number is standing in the exact middle of the line, a millionaire moving into a neighborhood doesn't change the house price of the middle home.

The Resistant Measures: Median and IQR is a Grade 6 math topic covered in Reveal Math, Course 1 in Module 10: Statistical Measures and Displays. Students at this level study the concept as part of their grade-level standards and are expected to explain, analyze, and apply what they have learned.

Because it only cares about which number is standing in the exact middle of the line, a millionaire moving into a neighborhood doesn't change the house price of the middle home. Therefore, when a data set contains an outlier, the median and IQR provide the safest, most reliable descriptions of the center and variation..