# MathBench>Environmental Science

## When size matters... (sample size, that is)

Determining sample size is very important. If your sample is too large, you will be wasting time and money. If your sample is too small, your results will not be very accurate. Like Goldilocks, you need the sample size that is “just right”.

When we collect sample data and take the average of those samples, it will usually be different from the actual population average. Yet as we increase the number of samples, their calculated average gets closer and closer to the actual average for the whole population. And if we take so many samples that we have sampled the entire population ... then the sample average would BE THE SAME as the actual average.

A simple way to determine the appropriate sample size is to graph a running average from the samples. Use the applet to add samples to the graph and watch the calculation for the number of dandelions counted per square. When you think you have a good estimate of the average number of dandelions in the square, click on "Stop Counting" and follow the directions.

Notice that the graph fluctuates then starts to level out. This happens EVEN IF the actual dandelions are unevenly spread. When it starts to level out, your sample size is probably big enough.

You may also notice (depending on how your computer is running today) that the estimate of population size is not always a very good estimate, even if you do everything right. This is what happens in real life as well. It's a bummer, but that's the tradeoff you get for not having to count every [gosh-darn] dandelion.