Measuring Center (Lesson 1.6)
Chapter 1 - Day 7
Find and interpret the median of a distribution of quantitative data.
Calculate the mean of a distribution of quantitative data.
Compare the mean and median of a distribution, and choose the more appropriate measure of center in a given setting.
Most students will already be familiar with the mean and the median and how to calculate each. The purpose of this lesson is to answer some new questions:
How does the shape of the distribution affect the relative locations of the mean and the median?
How do the mean and median change when an outlier is introduced into a data set?
Which measure of center (the mean or the median) is best to use?
Students will use this applet to make dotplots and get summary statistics.
Most students learn mean, median, and mode together in middle school. They often want to say that all three are measures of center. This is not necessarily the case. The mode could be near the center of the distribution but could certainly be anywhere else in the distribution. Thus, mode is not really a measure of center.
Many students know the “crossing off” approach to finding the median, where they cross off values on either end of an ordered list until they get to the middle. Be sure they know what to do if there are two values in the middle (take the average!). Be sure that students can interpret the median as “about 50% of the values are less than _____”.
A quick note about notation: x̄ is the mean of a sample, the Greek symbol μ is the mean of a population.
Use this applet to give students a visual representation of what is happening to the mean and median when an outlier is added to a data set. You can also drag the outlier left and right and the mean and median change dynamically.