Unit 8, Lesson 14
Comparing Mean and Median
Grade 6
Preparation
Lesson Narrative
In this lesson, students investigate whether the mean or the median is a more appropriate measure of the center of a distribution in a given context. They learn that when the distribution is symmetrical, the mean and median have similar values, so the mean should usually be used for its connection to fairness. When a distribution is not symmetrical, however, the mean is often greatly influenced by values that are far from the majority of the data points. In this case, the median may be a better choice.
At this point, students may not yet fully understand that the choice of measures of center is not entirely black and white, or that the choice should always be interpreted in the context of the problem (MP2) and should hinge on what insights we seek or questions we would like to answer. This is acceptable at this stage. In upcoming lessons, they will have more opportunities to include these considerations into their decisions about measures of center.
- Choose which measure of center to use to describe a given data set and justify (orally and in writing) the choice.
- Explain (orally) that the median is a better estimate of a typical value than the mean for distributions that are not symmetric or contain values far from the center.
- Generalize how the shape of the distribution affects the mean and median of a data set.
Let's compare the mean and median of data sets.
Required Materials
Activity 2
Required Preparation
For ”The Tallest and Smallest in the World” activity, students will need the data on their heights (collected in the first lesson). Consider preparing a class dot plot that shows this data set to facilitate discussions.