学生成绩分析中最优试卷样本量确定的研究

Determination of Optimal Sample Size in Student Achievement Analysis

本文应用简单随机抽样的理论来确定用于学生成绩分析的试卷样本抽取量,并得到相应的计算公式。在置信度为95%的条件下,计算不同相对误差下的样本均值和标准差,并与总体的均值、标准差进行对比分析,最终得到在7.5%相对误差下,对于人数不超过40班级,建议试卷的最优样本量确定为10。

Based on the theory of simple random sampling, the paper discusses the ways and means to determine the quantity of samples used for the analysis of students’ scores, and obtain the corresponding calculation formula. Under the confidence level of 95%, the sample mean and standard deviation under different relative errors are calculated and compared with the overall mean and standard deviation, and the relative error is finally obtained under the relative error of 7.5%.For the class size of no more than 40, the recommended sample size is 10.