1. 极端分数：全距受影响最大，四分位距受影响最小。
There are extreme scores in the data set: the full range is the most affected, and the quartile is the least affected.
2. 样本大小：全距可能随n增加而增加，四分位距和标准差不会。
Change the sample size: the full distance may increase with the increase of n, but the quartile distance and standard deviation will not.
3. 样本选取：同一总体多次选取不同样本，全距没有稳定的值，但四分位距和标准差是稳定的。
Select different samples: the same population selects different samples many times, the full distance has no stable value, but the quartile distance and standard deviation are stable.
4. 当存在不确定值的分布时，全距和标准差无法求得，四分位距可求。
When there is a distribution of uncertain values, the full distance and standard deviation can not be obtained, and the quartile distance can be obtained.
| 优点 (Pros) | 缺点 (Cons) | |
|---|---|---|
| 全距 (Range) | 1. 计算便捷 | 1. 样本稳定性差 2. 受极端数值的影响 3. 可能与样本量有关 |
| 四分差 (Interquartile range) | 1. 不易受极端分数的影响 2. 适用于有不确定值的数据 | 1. 在一定程度上样本稳定性差 |
| 标准差 (Standard deviation) | 1. 样本稳定性好 2.包含最多的信息 | 1.受极端数值的影响 |
| Pros | Cons | |
|---|---|---|
| Range | 1. Easy to Calculate | 1. Poor sample stability 2. Influenced by extreme values 3. Possibly related to sample size |
| Interquartile range | 1. Less susceptible to extreme values 2. Suitable for data with uncertain values | 1. Poor sample stability to some extent |
| Standard deviation | 1. Good sample stability 2. Contains the most information | 1. Influenced by extreme values |