In daily life, it is often necessary to estimate the yield of crops, such as estimating the yield per mu of rice. The common method is to harvest a small part of crops, such as 1 mu (1 mu = 10/mu), calculate the yield, and multiply it by 10 to get the yield of 1 mu. In order to reduce the error as much as possible, it is often to harvest several crops in different plots, take the average value after measuring the yield, and then use the average value to estimate the total yield per mu.

The yield of rice and other crops can be considered to be uniform, and the yield of different plots is similar, which can be estimated by the above method. But if you want to estimate the number of fish in a pond, the above method will not work. Because there are fish swimming everywhere in the pond, and the number of fish in different places is different, it is of course impossible to catch all the fish in the pond and count them. So, how is the number of fish in the pond estimated?

There is a clever way to grab some fish from the pond at will, such as 100 fish, mark it and put it back in the pond. After a period of time, it can be considered that these marked fish swam to all parts of the pond or were evenly distributed throughout the school. At this point, catch some more fish, such as 50, and count the number of fish that have been marked, assuming that two of them have been marked. Now, it is known that 2 of 50 fish are marked, that is, the number of marked fish accounts for 250 of all fish. So, a total of 100 fish (in the pond) were marked? This is easy to calculate,

100÷(2÷50)=2500,

Therefore, there are about 2500 fish in the pond.

Similarly, in order to minimize the error, we can also catch some fish at different times and in different places, count the number of marked fish, calculate the proportion, find the average of these proportions, and then calculate the total number of fish in the pond. For example, if you fish five times, the proportion of fish marked each time is 250, 370, 565, 438+000, 380 and 475 respectively. After calculation,

15(250+370+5 100+380+475)≈0.0447,

100÷0.0447≈2237

Therefore, there are about 2237 fish in the pond.