IM 6.8.10 Lesson: Finding and Interpreting the Mean as the Balance Point

Author:GeoGebra Classroom Activities, IM 6 – 8 Math

Which expression does not belong? Be prepared to explain your reasoning.

Here is the data set from an earlier lesson showing how long it takes for Diego to walk to school, in minutes, over 5 days. The mean number of minutes is 11.

Represent Diego’s data on a dot plot. Mark the location of the mean by using red triangle.

The mean can also be seen as a measure of center that balances the points in a data set. If we find the distance between every point and the mean, add the distances on each side of the mean, and compare the two sums, we can see this balancing.

Record the distance between each point and 11 and its location relative to 11.

Sum of distances left of 11: ___________ Sum of distances right of 11: ___________

What do you notice about the two sums?

Can another point that is not the mean produce similar sums of distances? Let’s investigate whether 10 can produce similar sums as those of 11. Complete the table with the distance of each data point from 10.

Sum of distances left of 10: ___________ Sum of distances right of 10: ___________

What do you notice about the two sums?

Based on your work so far, explain why the mean can be considered a balance point for the data set.

Here are dot plots showing how long Diego’s trips to school took in minutes—which you studied earlier—and how long Andre’s trips to school took in minutes.

The dot plots include the means for each data set, marked by triangles. Which of the two data sets has a larger mean? In this context, what does a larger mean tell us?

Which of the two data sets has larger sums of distances to the left and right of the mean?

What do these sums tell us about the variation in Diego’s and Andre’s travel times?

Here is a dot plot showing lengths of Lin’s trips to school.

Calculate the mean of Lin’s travel times.

Complete the table with the distance between each point and the mean as well whether the point is to the left or right of the mean.

Find the sum of distances to the left of the mean and the sum of distances to the right of the mean.

Use your work to compare Lin’s travel times to Andre’s. What can you say about their average travel times?

What about the variability in their travel times?