The Ultimate Decision Matrix (Look Before You Calculate!)
When interpreting graphical data displays in 6th grade statistics, the shape of the graph tells you which statistical tools to use. Symmetric distributions without outliers call for the mean and MAD. Skewed distributions or data with outliers require the median and IQR. Categorical data uses the mode. This decision matrix from Reveal Math, Course 1, Module 10 saves students from choosing inappropriate measures and producing misleading summaries of their data.
Key Concepts
The whole point of interpreting graphical displays is to let your eyes do the work before you do any math! Once you look at the shape of the graph, you immediately know which statistical tools to use: If the graph is Symmetric : Use the Mean (for center) and the MAD (for spread). If the graph is Skewed or has Outliers ( ) : Use the Median (for center) and the IQR (for spread). If the data is Categorical (words): Use the Mode .
Common Questions
Which measure of center should I use for symmetric data?
Use the mean for symmetric data without outliers. The mean is calculated using every value equally, which gives an accurate representation when data is evenly distributed.
Which measure of center should I use for skewed data or data with outliers?
Use the median for skewed data or data with outliers. The median is based on the middle position, so extreme values do not pull it away from the typical value.
What is the best measure of spread for symmetric data?
Pair the mean with the Mean Absolute Deviation (MAD) for symmetric data. Both are calculated using every value, so they work together consistently.
What is the best measure of spread for skewed data?
Pair the median with the Interquartile Range (IQR) for skewed data or data with outliers. Both are position-based and resistant to extreme values.
How do I quickly decide which statistical tools to use?
Look at the graph before doing any math. If it is symmetric, use mean and MAD. If it is skewed or has outliers, use median and IQR. If data is categorical, use mode.
When do 6th graders learn this decision matrix?
The decision framework for choosing measures of center and spread is covered in Module 10 of Reveal Math, Course 1.