value and the resulting differences are divided by MAD (see below). The calculation of MAD is done in three stages. First, the median is subtracted from each data point. Next, the absolute values of the differences are obtained. These are called the absolute deviations. Finally, the median of the absolute deviations is calculated and multiplied by the constant 1.483 to obtain MAD6.
阶段1—应用Hampel规则的第一步是将数据正态化。然而，不是使用将每个数据减去平均值后再除以标准偏差，而是将每个数据减去中位值后用差值除以MAD（参见下文）。MAD的计算有3个步骤。首先，每个数据减去中位值。然后，取差值的绝对值。这些值被称为绝对偏差。最后，计算绝对偏差的中位值，再乘以常数1.483来得到MAD6。
Step 2—The second step is to take the absolute value of the normalized data. Any such result that is greater than 3.5 is declared to be an outlier. Table 4 summarizes the calculations.
阶段2—第二个步骤是计算正态化数据的绝对值。任何超过了3.5的结果都被识别为异常值。表4汇总了计算。 The value of 95.7 is again identified as an outlier. This value can then be removed from the data set and Hampel's Rule reapplied to the remaining data. The resulting table is displayed as Table 5. Similar to the previous examples, 99.5 is not considered an outlier.
95.7再次被识别为异常值。这个值可以从数据组中除去，对剩余数值再次应用Hampel规则。计算结果显示在表5当中。与前面的例子相同，99.5未被识别为异常值。
Table 4. Test Results Using Hampel's Rule
Median = MAD = Data 100.3 100.2 100.1 100 100 100 99.9 99.7 99.5 95.7 100 n = 10 Deviations from the Median 0.3 0.2 0.1 0 0 0 ?0.1 ?0.3 ?0.5 ?4.3 Absolute Deviations 0.3 0.2 0.1 0 0 0 0.1 0.3 0.5 4.3 0.15 0.22 Absolute Normalized 1.35 0.90 0.45 0 0 0 0.45 1.35 2.25 19.33
Table 5. Test Results of Re-Applied Hampel's Rule
6
Assuming an underlying normal distribution, 1.483 is a constant used so that the resulting MAD is a consistent estimator of the population standard deviation.T