Samples Jump Around

On the last day of working with our students, we did an activity to represent that samples jump around.  For our activity, we had 100 random numbers for 3 different cities: Zeeland, Grand Rapids, and Holland.  Each number was representative of the number of pets in a household of that city.  We had the students choose 10 numbers out of their data set.  We had them calculate the mean, the TAD and the MAD.  We didn't have a lot of time to explain the goals of the activity, as it got crunched into the last few minutes of our lesson.  I would really like to run the activity again for a longer session and touch on things like how samples jump around, the variability of each data set, the "one MAD rule of thumb", and other statistical concepts.

The lesson would be:

1. Distribute random number samples of a couple different cities.
2. Have the students randomly choose 10 numbers.
3. Have students calculate the mean.
4. Have students calculate the TAD.
5. Have students calculate the MAD.
6. Sort data into 3 columns on the board for each city.  Have students record their data for their city.

As a class, discuss the data.

Questions to Ask:

• "What are similarities/differences overall?"
• "How can we decide if there is a difference between the number of pets per household in each city?"
• "Could we get the same mean or MAD in all three cities? What does that tell us about the population?

Introduce or Review "One MAD Rule of Thumb"

Discuss how samples jump around... "what does this mean for things like polls, like in magazines or online?"

Discuss factors of variability

Extensions:

Find newspaper, magazine or online polls and ask them to evaluate them for their classroom to see how likely the results are to happen again.

In my opinion, this activity would go along well with the GAISE report.  I think that this activity has a lot of real world relevance which is kind of the point of studying statistics, according to the report.  We want students to be able to thrive and I believe that understanding this information about samples and collecting data and studying data is really important.