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利用样本极差W估算标准差6的优点是运算简便,且样本大小n很小时,估计效率也颇高(表1)。估算的依据是,W的数学期望与6成正比,所以可用W/dn作为标准差的一个无偏估计。这里的dn为W/6的均值,其值见表2的第二行。笔者曾用大兴安岭得尔布尔林业局的面积为0.06公顷的样地材积资料,考察了W和6的正比关系。通过选取的大小分别为5～35的84个样本,发现散点分布大致呈直线关系,其直线式为du=2.16+0.0634n(r=0.77)利用上式算得不同n的do值如表2第三行从表2可以看出,理论值是有实践基础的。可以说W和6具正比关系。
The advantage of using the sample range W to estimate the standard deviation 6 is that it is computationally simple and the estimation efficiency is high when the sample size n is small (Table 1). The estimate is based on the mathematical expectation of W being proportional to 6, so W / dn can be used as an unbiased estimate of the standard deviation. Here dn is the average of W / 6, the value of which is shown in the second row of Table 2. The writer once used the area of 0.06 hectare plot data of Dabur Forestry Bureau of Daxinganling to examine the direct relationship between W and 6. By selecting 84 samples of 5 ~ 35 respectively, we found that the scatter distribution has a linear relationship with du = 2.16 + 0.0634n (r = 0.77) The third line can be seen from Table 2, the theoretical value is based on practice. It can be said that W and 6 have a direct relationship.