中学物理成绩信息熵的计算

Calculation of the Information Entropy of the Examination Scores of Physics in Middle Schools

通过对离散型及连续型随机函数的信息熵的分析,提出了信息熵计算的基本方法.研究发现,中学物理成绩具有不同的分布特征,有正态分布、瑞利分布、均匀分布等,有的甚至不能用常见的概率分布函数描述.对这些容量大小不同、分布特征各不相同的样本,都可以得到合适的信息熵,显示了计算方法的广泛适用性.

The samples in our study are the examination scores of physics in middle schools. A new method for the information entropy calculation is presented by using the discretization of the information entropy of continuous random variables,and was applied for the calculation of the information entropy of the samples. The distribution of the samples was also discussed. It is showed that these scores do not obey the same distribution,such as the normal distribution, Rayleigh distribution, an uniform distribution func-tion ,and so on. It is also showed that the present method can be useful in the calculation of the informa-tion entropy of the samples with different sample size and distribution. So it is very useful for the calcula-tion of the information entropy of the samples in other fields.