Extract a perfectly random sample from a population, and what will you get? Many people think such a sample will be just like the population, but smaller. They expect the sample to be a “miniature population.” Bad thought. Most likely, the numerical characteristics of the sample will not match exactly those of the population.
If you randomly select 16 people out of a population containing as many males as females, what kind of gender split should you expect in the sample? Don’t predict 8 males & 8 females! That’s because the odds are about 4-to-1 AGAINST having the sample be perfectly balanced gender-wise.
To prove to yourself that a sample is not likely to end up being a small mirror-image of the population, conduct a little coin-flipping experiment. You can do this quickly via a computer simulation available through the link below. After you get to the “Simulating Coin Tossing” applet created by Allan Rossman & Beth Chance, click on the gray, rectangular button labeled “16 Tosses.” This will cause the computer to (a) flip 16 fair coins, (b) show you, simultaneously, the result of each flip, and (c) put a dot in the graph to indicate the number of heads contained in the sample. Click the “16 tosses” button several more times, and watch what happens as additional dots are put into the graph. You will see, especially after clicking the “Show Tallies” button, that the majority of samples produced something other than 8 heads and 8 tails, even though the coins being flipped were fully unbiased.