等间距线性数据的标准偏差

摘要

Two types of linear dates have been distinguished. The standard deviation has been calculated by method of the mean values,the successive minus and the least squares respectively,there comparison has been given.For the first kind of linear dates,the independent errors with equal rights is derived from the measures of the locations and has nothing to do with the position measurement in different place,the method of least squares gives the minimal standard deviation.For the second type of linear dates the independent errors with e-qual rights is derived from the increment in the process of measuring,the method of arithmetic mean gives the minimal standard deviation.%对大学物理实验中两种不同类型的等间距线性数据进行了区分。第一类线性数据中，等权独立的误差来源于对每一位置的测量而与其它位置的测量无关，应该把每一测量点对最佳直线的偏离作为研究对象，其它参量的标准偏差应该从该对象的标准偏差为出发点求得；第二类线性数据等权独立的误差来源于每一次测量过程的增加量，应该把每一次测量的增加量同最佳增加量的偏离作为研究对象，其它参量的标准偏差应该从此对象的标准偏差为出发点求得。针对这两类数据，分别按照算术平均值法、逐差法和最小二乘法的原则进行处理，给出了符合其数据类型对象的最佳斜率表达式和它们的标准偏差表达式。给出了它们的比较：第一类线性数据的最小二乘法处理的最佳斜率的标准偏差最小；第二类线性数据的算术平均值处理给出的标准偏差最小。