The Ultimate Pairing Guide
In 6th grade statistics, measures of center and spread must be paired correctly. The mean is always paired with the Mean Absolute Deviation (MAD) for symmetric data without outliers. The median is always paired with the Interquartile Range (IQR) for skewed data or data containing outliers. Mixing them — such as reporting a median paired with a MAD — is statistically inappropriate. This pairing rule from Reveal Math, Course 1, Module 10 helps students produce accurate and meaningful data summaries.
Key Concepts
When we describe a data set, measures of center must be properly paired with their corresponding measures of variation based on the shape of the data.
No Outliers (Symmetric Data): Pair the Mean with the Mean Absolute Deviation (MAD) .
Common Questions
Why must measures of center and spread be paired correctly?
Mean and MAD both use every data value, so they are both sensitive to outliers. Median and IQR both use ordered positions, so they are both resistant to outliers. Pairing them correctly ensures consistent and meaningful analysis.
What measure of spread goes with the mean?
The Mean Absolute Deviation (MAD) is paired with the mean. Both are calculated using every single value in the data set, giving them the same strengths and weaknesses.
What measure of spread goes with the median?
The Interquartile Range (IQR) is paired with the median. Both are position-based measures that are not distorted by extreme outliers.
Is it wrong to report a median with a MAD?
Yes. Reporting a median paired with a MAD is an inappropriate pairing. The median should always be paired with the IQR because they are both resistant to outliers in the same way.
How do I decide which pair to use for a data set?
Look at the data for outliers or skewness. If there are no outliers and the data is roughly symmetric, use mean and MAD. If there are outliers or the data is skewed, use median and IQR.
When do 6th graders learn about pairing measures of center and spread?
Module 10 of Reveal Math, Course 1 covers this in the Statistical Measures and Displays unit.