It’s complicated to tell things that keeps moving – imagine a pastor who has to tell all of his sheep. What counts on it is the existence of a mathematical trick that helps to have control over your flock.
Whether it is sheep or matches inside a box, it is difficult to count objects that move.
Fortunately, there is a technique that allows you to calculate the number of objects without having to tell them ‘one by one’.
In an article in, mathematics Katie Steckles Teach us a trick for Count “Carpenter animals”.
Capture-reclapth
Or method of capture-reclapth It consists of obtaining a sample. For example, in the case of the pastor, expect some sheep to pass and then collect some – mark individuals differently and then free them in the population.
After a while, the process is repeated to choose another group of sheep and are counting how many of them are already marked.
We captured, say, 50 animals initially and marked them all, and then, in the recapture step, found that half of the animals he saw were marked, it tells him something about the entire population.
Since half of the sample is marked, this implies that half of the entire population is marked – therefore, There must be about 100 individuals.
This can give a “Reasonably exact estimate” – writes the mathematician – of a population, without having to find and count each of its members.
During World War II, allied statistics wanted to determine the number of tanks the German army was producing. The captured tanks could not be relaunched, but as the components of the tanks are marked with series numbers, another approach allowed them to estimate.
They recorded the serial numbers of all tanks captured or destroyed, based on the principle that they were numbered sequentially and randomly distributed. If the largest number of serial in your data is l and the number of captured tanks is n, an estimate of the total number of tanks is given by:
L + L/N
Thus, Katie Steckles explains, if we had four numbers, the largest of which was 80, we could assume that the whole range extends for another 80/4 = 20, so there would be about 100 tanks in total.
This is known as the “German tank problem”in statistics.
Experience of Cantina forks
Steckles says he gives the example of a colleague, who asked his students to calculate the number of forks in the school canteen – impossible to tell because some time will be used and others will be washed.
Your class “captured ”a set of forks and marked each one of them With a drop of nail varnish, releasing them after again in the population.
A week later, they recaptured another sample of the population and used it to estimate the total number of forks.
