Frequency method contains the most important conclusion in probability theory. Is the basis of modern statistics.
Frequency-The frequency at which random events occur in the whole event.
Random Event/Global Event = Frequency
3. The underlying logic of1frequency method: there is a real and objective probability of a random event. As long as there is enough data, the calculated frequency will be infinitely close to this real and objective probability. -The law of large numbers in mathematics
What mathematics wants is not empirical conclusions, but complete reasoning and proof based on logic. The biggest difference between mathematics and many disciplines is also here. In mathematics, experiments and observations are never allowed to verify the correctness of a question or conclusion, and mathematical conclusions can only be drawn through logical deduction and proof.
The law of large numbers also proves that it is feasible and reasonable to predict the future with historical data through repeated experiments in the same environment.
There is enough data-how much?
The law of large numbers has enough data, which is an infinite (or infinitesimal) concept and will never be reached. However, if it is to be applied to real life, it must be given certain "restrictions". Mathematicians have set two concepts: one is called "precision error" and the other is called "confidence".
Precision error: the fluctuation range of specific data;
Confidence: the proportion of samples within the precision error range.
Through these two restrictions, some errors can be tolerated, which can greatly reduce the number of experiments or the amount of data collected.
In reality, almost all data surveys and statistical results have the following characteristics:
① Based on the underlying logic of "measuring probability by frequency";
(2) Compromise the probability accuracy to some extent.
When students are employed every year, the higher authorities of the school require the employment rate of each school (including employment, postgraduate entrance examination, going abroad, etc.). ) should not be less than 83%. I think this data should be based on the probability given by the frequency method. That is to say, in a certain period of time (such as the last five years), the number of employed people counted by the labor department every year is divided by the total number of graduates in the country. But I don't know the precision error and confidence of this probability.