Main --> In the Classroom: Statistics

Standard Error (Demonstration courtesy of John Kulig via TIPS.)

An easy non-computerized demo is have everyone in the class put their height in inches or cm on a slip of paper into a hat, and then sample one by one and plot them on the whiteboard (sample with replacement). How you "figure" the standard deviation depends. I like to have the actual values in advance, but if not, the "idea" of the standard deviation can be eye-balled from the plot, as well as the mean.

Then you can do the same thing by having someone take out 2 slips of paper at a time and get repeated averages of two heights, plotting the averages on a separate plot on the whiteboard.  Again, I like to know the means and standard deviations in advance so I can stack one plot above the other with the means and x-axis values lining up. It can be done with means of 4 or 8 too, but that takes more time. If done carefully, it's easy to see that roughly 2/3 (68%) of X fall within one SD on the X plot, and 2/3 of means lie within one SE on the means plot - with the usual caveat "individual results may vary".

When I do this in a stats class (different audience), I sometimes generate random data on MINITAB for a few different sample sizes and pop the histograms out of the computer, and often use sample sizes 1 to 4 to 16, as I can wing the standard error in my head (SE gets chopped in half every time N increases 4-fold, so, if you use IQ scores you can jump from 15 to 7.5 to 3.75 without calculators or computers).

If all else fails, my moment of Zen (I do one every stat class). On this topic: "Standard Deviation is to X as Standard Error is to X bar".