8.2 Five marbles and the standard error of the mean


Materials required are marbles and a 200 gram scale.


This term a mix of marbles was used. 


Students were told to pick five marbles. This avoided an issue that had been created by giving students five of the same marbles. When different sets of five were in use, some were the smaller, lighter blue marbles and these would generally not capture the population mean.

A spreadsheet, single tab for the Smartboard memory limitations, is used to generate data. Tallying a dozen students took until around 9:25, this photo was taken at 9:32. 

After the first five marbles were massed the point estimate of the population mean was 5.06. The massing was paused to explain that this was the best estimate of the population mean for that student. The point estimate for the population mean. 


Masses are done marble by marble. After the second student the split in the point estimate was pointed out. And that both were now "wrong" - the population mean was 5.08 after the second student. 


Some basic statistics used in the frequency table.



No student had a sample mean, and thus a point estimate for the population mean, of 5.1683 grams. Yet the 95% confidence interval for each student captured that value. 


This was the chart under the Smartboard sketch above.

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