Choosing the Best Measure of Center
The best measure of center depends on the shape of the data. Use the mean when data is roughly symmetric with no outliers — it accurately represents the typical value. Use the median when data is skewed or contains outliers — extreme values distort the mean but not the median. For example, five house prices of 200k, 210k, 225k, 240k, and 950k have a mean of 365k (misleadingly high) but a median of 225k (accurate). Use mode for categorical data like favorite pizza toppings. This decision skill from Reveal Math, Course 1, Module 10 is foundational for 6th grade statistics.
Key Concepts
Having three ways to find the center (Mean, Median, Mode) means you must choose the best tool for your specific data: Use the Mean when the data is roughly symmetric (evenly spread out) with no extreme outliers. Use the Median when the data is skewed or contains outliers (extremely high or low numbers), because the median ignores extreme values. Use the Mode for categorical data (words, not numbers) or when you specifically want to know the most popular choice.
Common Questions
When should I use the mean vs. the median?
Use the mean when data is symmetric and has no extreme outliers. Use the median when data is skewed or contains outliers, because outliers pull the mean away from the typical value but do not affect the median.
Why does the median resist outliers better than the mean?
The median is based on position (the middle value), so extreme values do not change it as long as they remain on the same side. The mean uses every value equally, so a very large or small number pulls it significantly.
When do I use the mode as a measure of center?
Use mode for categorical data (words or categories) where you cannot calculate a mean or median, such as finding the most common favorite color or most popular topping.
Five test scores are 70, 75, 80, 85, 90. Which measure of center is most appropriate?
The mean is most appropriate because the data is symmetric with no outliers. Mean = (70+75+80+85+90)/5 = 80, which is also the median.
House prices are 200k, 210k, 225k, 240k, 950k. Which measure is best?
The median (225k) is best because 950k is an outlier that pushes the mean up to 365k, making it unrepresentative of a typical house price.
When do 6th graders learn to choose the best measure of center?
Module 10 of Reveal Math, Course 1 covers this in the Statistical Measures and Displays unit.