----- Forwarded message from Simon, Steve, PhD -----
Trevor Watson writes:
>I am still looking for a simple formula explanation for lower high >school students as to why a sample size does not have to be large - even >for a very large population.
It's not a formula, but I like the explanation that was used in an ASA presentation about Statistics. It goes something like "Any good cook knows that a single sip of a well stirred soup will tell you how good the entire pot is".
The converse statement is also interesting. It doesn't matter how much of the soup you taste if it isn't mixed well (i.e., a non-random sample of just about any size is useless).
Steve Simon, firstname.lastname@example.org, Standard Disclaimer.
----- End of forwarded message from Simon, Steve, PhD -----
This suggests an activity if you can afford several large bags of M&Ms and have a big salad bowl. First, sort the M&Ms and count how many you have of each color so you know the population proportions. Then dump them in the bowl one color at a time. With little or no mixing, have blindfolded students scoop out a cup and check the sample proportions. You should see extremem bias toward the color you dumped in last. Then try various degrees of mixing. When they are very well mixed you can check the effect of sample size on sample-to-sample variability by taking many samples.
Another inspiration for this activity is the fact that (IMO) typical bags of M&Ms are NOT random samples from the population because they are not mixed well enough. Now Mars claims they are well mixed, but it is well known that people tend to underestimate how much mixing is required. (See the draft lottery data.)
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