This InspireData lesson focuses on interpreting the mean and median values of a set of data, and understanding the impact of the shape of data and outliers on these values. The activity uses the Produce Predictions database found in InspireData (InspireData Starter Screen>Databases>Mathematics>Produce Predictions). The attached file provides sample slides.

Lesson:
• Optional: Add fields in Table View and use the Formula Editor to convert length, girth and weight to customary units or to other units within the metric system.
• Create an Stack Plot of Weight. Ask students to describe the shape of the graph, and any general trends they observe. (Try changing the Step to observe how different intervals on the axis impact the shape of the data and provide more or less precise information. For Weight in grams, settle on a Step interval of 500).
• Can they guess which produce items are heaviest? Individual icons can be labeled by right clicking and selecting “Label Selected Icon” and marked using the Mark Icon tool. Label and mark any outliers.
• Add the Mean and Median to the plot. Which value is higher? What does the median represent in the context of this situation, and what does the mean represent? Why is the mean higher than the median for this data? (The heaviest produce items bring up the average. Most fruits and vegetables actually fall between 0 and 500 grams, which is why the median, or middle value, is 231 grams. But the watermelon, at almost 9000 grams, brings up the average to 721 grams).
• Exclude the outliers that have been marked by right clicking and selecting “Exclude Selected Icons.” Exclude one outlier at a time and note what happens to the mean and median. Why is the mean dropping noticeably? Why are the median and mean values getting closer together? Which value do outliers impact the most?
• This process can be repeated for Length and Girth. Optional: If students have access to computers, divide the class into pairs and have them finish the activity by making the plots themselves and using the Notes Area and the Slide Sorter to document their work and analysis.

This activity was created using InspireData 1.5, which must be installed to open the file. Download a 30-day free trial at href="http://www.inspiration.com/freetrial">www.inspiration.com/freetrial or if you have InspireData 1.0, download a complementary upgrade.