abstract

Nowadays, with the rapid development of the world, the competition in all walks of life is becoming more and more fierce. In order to reflect fair competition, it is always necessary to evaluate enterprises or individuals. However, due to the limitation of funds and resources, we can't and don't need all appraisers to evaluate all the evaluated enterprises or people. Therefore, only partial evaluation results can be obtained. What this paper wants to solve is how to use these results for in-depth analysis and get a fair ranking.

This paper is to solve the sequencing problem under the condition of a large number of participants. If the quantity is not large, we can let all the appraisers evaluate all the evaluated enterprises or people. For all evaluated enterprises or people, if the number is sufficient, the final result data basically obeys normal distribution. Therefore, we can use the properties of normal distribution to solve this problem.

Keywords: Normalized analysis and prediction of normal distribution data distribution

I. Restatement of the problem

In all kinds of competitions, appraisals and other activities, the ranking of contestants will always involve the end. For example, the mathematical modeling competition has many teams and a large number of papers need to be reviewed. Because of the time, it is impossible for every reviewer to read all the papers, only a part of them and give his own score. Finally, according to the incomplete reports of these judges, the final ranking of all the contestants is given. Although reviewers can give marks fairly, due to individual differences, there are some problems as follows: each reviewer has different habits of giving marks, some reviewers like to give high marks, all papers have high marks, and some are just the opposite; Some reviewers' scores vary greatly, while others are concentrated; Obviously, due to the difference of teachers' level, the random error of each person's score is not the same. Try to establish a mathematical model to solve the ranking problem and apply it to the following data (see attachment 1) to give the final ranking.

Second, the problem analysis

When determining the ranking of contestants, due to the differences in grading habits and other levels of judges, different scores will be given, and it is impossible to directly judge the ranking of each paper only by reading some papers.

Therefore, we should first look for a criterion, then each judge will launch a series of standard score according to his own score and this criterion, and finally we can judge the ranking directly through the above-mentioned standard score. In this model, probability theory and mathematical statistics can be used. Firstly, each group of samples is standardized to obtain the standard normal distribution. Then, according to the reviewer's scoring habits and concentration (which can be reflected by the mean and variance of data here), the score of one reviewer is used to analyze the possible achievements of others in the same paper.

For example, for the paper numbered PN00 1, the score of No.5 reviewer is 7 1, and the specific scores of the other five reviewers can be statistically analyzed by using the above standardized results. For another example, PN003' s paper only has reviewer 3 and scoring. According to standardization, the scores that other four people will give in this paper can be deduced.

According to the above method, the possible scores of each reviewer in this 100 paper (including the original data, that is, the data given in the model) are statistically analyzed, and the average value is taken to get a complete report. Finally, the data of each line is statistically analyzed (because each reviewer gives a score, the average score can be used) to determine the final ranking of the paper.

There are too many others.