Purpose:  Calculate the total number of beans in a sample based on random samples of the population.

Procedure:  Each group of four students received a sample bag containing white beans and a bowl of red beans to use to replace the tagged population.  First we decided who would fill each job for the group.  The jobs were sampler, mixer, counter, and recorder.  The sampler reached into the sample bag and removed a hand full of white beans.  (We found out later why the directions said to remove a small handful of beans.)  Next the counter counted the beans.  There were 220 of them.  We counted out 220 red beans to replace the white beans in the original sample and returned the red beans to the bag.  We put the white beans in the collection bowl at the front of the room.  The recorder wrote down that their were 220 beans in the original sample.  Then the mixer closed the plastic bag and shook up the red and white beans until they were mixed up good.  After that the sampler chose another handful of beans.  We made sure he picked a smaller hand full this time so there wouldn't be so many.  The counter counted a total of 64 beans, 18 of which were red.  The recorder recorded the numbers.  Then the sampler returned the beans to the bag and the mixer sealed it and shook it up.  We repeated this procedure until we had numbers for ten recaptured samples.  Then we counted all of the beans in the sample, removed the red beans and put them back in the bowl, turned in our materials, checked out calculators, and began making our calculations.  We had to find the mean of the total recaptured beans and the mean of the red beans recaptured.  Then we used the means and the original figures in a proportion to estimate the number of beans in the sample.

Data:

By adding up all of the data in each column, we got the total, then we divided the totals by 10 to get the means.

We then used the following proportion to calculate an estimate for the population:

Initial capture is to total population as mean of red recaptured is to mean of all recaptured.

220/P = 17/61

We used the cross products to get the following equation:       17P = 13420

Next we divided both sides of the equation by 17 to get:    P =  789

Discussion:  Our calculated sample estimate of 789 compared favorably with the actual sample count of 793, so it looks like the capture-tag-recapture method would be a pretty accurate method for sampling wildlife or fish, where it isn't possible to actually count every single animal.  We may have lost or gained some beans in our actual sample count because once when the mixer was shaking the bag it wasn't sealed and the beans went everywhere, so we had to go around the room and clean up our mess.  It is possible we either didn't get all of our beans back  because we overlooked them or someone else got them.  It is also possible we picked up beans that belonged to some other group.  If we ever do this again we will remember that it is important to make sure the bag is sealed completely.

Conclusion:  The Capture-Recapture method can accurately estimate a population if it is used the right way.