When scientists want to know the number of living things in a given area they can select from several different methods.  The most accurate data for plant species in a given area is obtained by counting the entire population.  In many cases counting the entire population is impractical and very time consuming.  A more practical method is to count a small sample of the population and expand the sample size to represent the entire population.  The resulting answer is an estimate of the population.

Sampling is an effective means of measuring a population when the estimate is a good one.  When the estimate is not a representative of the population you have a problem.  This activity will help students grasp the concept of sampling and determine problems you can have with sampling techniques.  Examples of using sampling are provided (PDF file requiring Adobe Acrobat Reader).

Hand out the page with lines running in every direction.  Allow students to determine what they are looking at.  There should be some interesting answers.  Lead them to where they can determine they are looking at tree roots.

Let's imagine we can go anywhere we want to view a forest.  Let's go down into the soil about six feet, Lay down, imagine all the soil gone, and look up toward the sky.  What do you see?  Is this a good location to sample the trees in the forest?  I could argue that it should be since about half of every tree is in the ground.  When we look at the distribution of tree roots in the ground we find a mat of roots tangled together going in every direction you can think of.  It would not be easy to sample trees by measuring their roots.  How many trees are there in the "spider picture"?  The answer is twenty.

An easier way to determine the number of trees is to walk among them and count them.  Another way is to look at the cross sections of each tree trunk.  Hand out the page with twenty black spots on it.  These spots represent the trunks of the twenty trees seen in the "spider picture" and move them around until the spots match where the roots come together to support tree trunks.

Counting the trees is simple when you have twenty trees.  What if you have 100 acres of trees with 14,700 trees?  Do you want to count them?  Let's assume the enclosed grid represents one acre.  Each square represents 1/100 of an acre.  We can use this grid to demonstrate sampling techniques.

When I placed the grid on the page of small dots I had 147 dots in the 100 squares.  If each dot represented a tree then there are 147 trees on the acre.  The number of trees in each column, starting with the left hand column is 9,  11, 24, 14, 10, 12, 11, 19, 18, 19 for a total of 147 trees.  If I make my sample to be one column, how many times will I have a good estimate of the number of trees present?  The answer is: Only once.  The other nine times will give me poor estimates.

What happens if I measured two rows selected at random?  I will get a good answer thirty percent of the time.  Sampling strips of a population is not a good idea when the distribution of the population is irregular such a with random of aggregate patterns of distribution.

Another sampling technique is randomly located plots throughout the population.  For example, select 10 plots on the attached grid and count the dots in all ten plots.  The sample size is the same as measuring one column.  By having randomly scattered the plots across the sample area we are able to get a better measure of the population.  Remember though, a sample is an estimate.  We can increase the accuracy of the sample by measuring 20 plots.

Break into groups, randomly select twenty plots on the grid and count the dots in your sample.  Share with each other your answers.  When you look at the variation in answers you can see why we call answers determined by sampling "estimates."

Foresters are always sampling trees.  How many reasons can you think of for sampling trees?

Tree density is a commonly sampled forest measurement.  Density is a measure of the square feet of solid wood growing on an acre.

Table 1: Tree density as determined by measuring the cross sections of tree trunks on one acre at 4.5 feet above the ground and the type of management favored by the listed density.

The square feet of wood on an acre is determined by adding together the amount of wood in each cross section.   Table 2 shows the square feet for a variety of tree sizes.

Table 2:  Square feet of wood in trees for different tree cross section diameters.

Assume you have 150 trees on an acre with 25 in each diameter mentioned above.  What is the basal area for the forest?  The answer is 108.25 square feet.

Is this a good forest for quail?  The answer is no, it is too dense and will reduce the amount of annuals that will grow producing seed and attracting insects.

If you removed the smaller trees, how many trees would you remove to get the ideal density for quail of 60 square feet?  The answer is 101 trees.  There would be 49 trees remaining.

There are many exercises students can do with sampling.  These are just a few.  Have fun with seeing the trees in a new and different way.