I discovered a great resource that visually helps to understand the 6th Grade Common Core Standards that develops understanding of statistical variability. The resource is a JAVA application called "Measures of Center" from www.maine.edc.org. The site looks like a sign-in site, but the applets/technology tool lists for student and classroom use are located at the bottom of the page and no login is required.
"Measures of Center" lets you explore mean, median, and mode through the use of an interactive line plot. Modify the line plot by dragging on Xs representing data. The measures of center are shown graphically and the values are computed dynamically as data is added to the graph. The maximum data can be adjusted to accommodate a wide array of values. One to ten data points can be displayed at a time.
I like that you can add pieces of data to the line plot and SEE the results of that additional data reflected in the median, mode, and mean immediately.
This applet will allow you and your students to see the results of how the measures change based on the data. What would be the effect of an outlier data point? What can I expect to be the effect on the measures of center when the data has a small spread? What can I expect when the data has a larger spread or range?
I think students need exposure to these types of questions so they can develop a sense of what to expect. How can they ask themselves if their answers make sense, if they can't predict an effect that is normal?
Explore these questions one day, and then the next day create a line plot and have student PREDICT what to expect if you add an outlier, have a small range of data points, have a large range of data points. Make them start to predict... and think about math not just calculate the mean, mode. or median.
I just bought a Jenn-aire refrigerator that had to be ordered and I waited for a period of 51 days for that appliance. I think Jenn-aire should look at the mean number of days that their customers wait for appliances that are ordered from their company. Is the spread of "number of days" that their customers wait for their products large or small? Are there outliers, and are those outliers satisfied with their customer service or be repeat customers in the future? Remember that mathematical questions are asked about everyday life situations because MATH MAKES SENSE OUT OF THE WORLD.