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====== 算术平均数 ======

算术平均数（mean）是最常用的，也是最容易理解的一个集中量数指标。

The mean is the most common and easiest to understand indicator of the measure of central tendency.

算数平均数的计算公式为：

The formula for calculating the arithmetic mean is as follows.

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考虑集中量数时，作为首选的集中量数，相比中数和众数，算数平均数的反应最灵敏、最客观且最具代表性。此外，算数平均数还可以进行代数运算，比如，每个观测量都加上一个常数时，算数平均数也会加上一个相同的常数；而每个观测量都乘上一个常数时，算数平均数也会乘上一个相同的常数。

The mean, which is the preferred choice when considering the measure of central tendency, is the most responsive, objective and representative when compared to the median and the mode. Additionally, the mean allows for algebraic manipulation. For example, when a constant is added to each observation, an identical constant is added to the mean as well. And when each observation is multiplied by a constant, the arithmetic mean is also multiplied by an identical constant

不过，如果数据中存在极端值，那么算数平均数的代表性会受到一定影响。

However, the representativeness of the mean is somewhat compromised if there are extreme values in the data.


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====== 中数 ======

中数（median）又被称为中位数，它将我们所研究的数据分为数目相等的两半，其中一半的值比它小，而另一半的值比它大。

The median divides the data into 2 halves with the same amount, one half smaller than it, while the other larger than it.

如果数列的总个数n为**奇数**，且最中间的值与相邻的值都不相等，那么最中间的，也就是第(n+1)/2个数就是这n个数的中数。如果n是**偶数**，按照惯例，可以取位于中间的两个数（第n/2个数和第n/2+1个数）的平均数作为中数。如果排列好后的数列分布的中间**有相等的数**，原则上将重复的数字看作一个连续体，利用中间数据的精确上下限进行插值法。

If the total of the data(n) is odd, and the number in the middle, the one in the position of (n+1)/2, is not equal to its neighbors, then it would become the median. If n is even, the mean of the 2 numbers in the middle(the two in the position of n/2 and n/2+1) would become the median, usually. If there exists several same numbers in the middle of the ordered data, in principle, they should be considered as a continuum, and use interpolation method to calculate the median by the accurate boundaries of that number.

中数只和位置有关，所以对数据变动的反应不够灵敏，不过这恰好使它不易受到极端值的影响。而且中数也不能进行代数运算。

The median only relates to the position in the data group, so it is not sensitive enough to the changes in data, but in the same time, the median is not easy to be affected by extreme numbers. The median cannot perform algebra calculations.

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====== 众数 ======

众数（mode）是指出现次数最多的那个数或类目，用M0来表示。//众数可能有不止一个。//

The mode is the number or genre to be most frequently appear, usually noted as M0. //There may exist more than 1 modes in a data series.//

众数也不易受极端值的影响，但是代表性比中数还差，也不可以进行代数运算，因而应用较少。

The mode is also not easy to be affected by extreme numbers, but its representativeness is weaker than median, and it also cannot perform algebra calculations, so the mode is less used in analysis.