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全距_标准差_四分位距

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全距_标准差_四分位距 [2024/03/11 04:40] – [标准差（standard deviation）] fairytaleee全距_标准差_四分位距 [2024/03/12 01:44] (当前版本) – [四分位距（interquartile range）] caomingsu
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   * 例子：若X是离散型，range=10-5=5；若X是连续型，range=10.5-4.5=6   * 例子：若X是离散型，range=10-5=5；若X是连续型，range=10.5-4.5=6
   * 全距的代表性较差，只依据两个极端值   * 全距的代表性较差，只依据两个极端值
 +  * Range  describes the fractional maximum distance in a distribution and is obtained by subtracting the exact upper limit of the maximum value of the distribution from the exact lower limit of the minimum value of the distribution. The value of range depends only on the two extreme values.
  
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   * 包含所有的信息，代表性强   * 包含所有的信息，代表性强
   * Standard deviation describes the distance of each individual in the distribution from a certain standard, which is the mean.It is the most important and commonly used amount of difference, contains all the information and is highly representative.   * Standard deviation describes the distance of each individual in the distribution from a certain standard, which is the mean.It is the most important and commonly used amount of difference, contains all the information and is highly representative.
-  - 离差 Dispersion+ 
 +  - **离差 Dispersion**
       * 定义：某数据点到均值的距离       * 定义：某数据点到均值的距离
       * 离差=X-μ       * 离差=X-μ
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       * 任何一个分布中所有个体的离差值之和必然为零       * 任何一个分布中所有个体的离差值之和必然为零
       * Dispersion is the distance from a data point to the mean,which is consists of positive and negative signs and numeric values.If the value is greater than the mean, the dispersion is positive; if the value is less than the mean, the dispersion is negative.The sum of dispersion values in any distribution must be zero.       * Dispersion is the distance from a data point to the mean,which is consists of positive and negative signs and numeric values.If the value is greater than the mean, the dispersion is positive; if the value is less than the mean, the dispersion is negative.The sum of dispersion values in any distribution must be zero.
-  - 和方 Sum of squares+ 
 +  - **和方 Sum of squares**
       * 定义：SS=∑(X-μ)²=ΣX²-(∑X)²/N       * 定义：SS=∑(X-μ)²=ΣX²-(∑X)²/N
       * 解决了正负符号的问题       * 解决了正负符号的问题
       *There are two ways to remove the influence of signs when we want to count the sum of the dispersion, take the absolute value or the square. The latter is much simpler in the implementation of computer operations, so it is widely used.       *There are two ways to remove the influence of signs when we want to count the sum of the dispersion, take the absolute value or the square. The latter is much simpler in the implementation of computer operations, so it is widely used.
-  - 总体的方差和标准差 Variance and standard deviation of the population+ 
 +  - **总体的方差和标准差 Variance and standard deviation of the population**
       * 定义：总体的方差是和方除以总体的容量，也被称为均方；总体的标准差是总体方差的平方根       * 定义：总体的方差是和方除以总体的容量，也被称为均方；总体的标准差是总体方差的平方根
       * 总体方差=σ²=SS/N       * 总体方差=σ²=SS/N
       * 总体标准差=σ=√(SS/N)       * 总体标准差=σ=√(SS/N)
       * The variance of a population is the sum squared divided by the capacity of the population, also known as the mean square; The standard deviation of the population is the square root of the variance of the population.       * The variance of a population is the sum squared divided by the capacity of the population, also known as the mean square; The standard deviation of the population is the square root of the variance of the population.
-  - 样本的方差和标准差 Variance and standard deviation of the sample+ 
 +  - **样本的方差和标准差 Variance and standard deviation of the sample**
       * 样本是从总体中抽取出的一部分，变异程度应该小于总体       * 样本是从总体中抽取出的一部分，变异程度应该小于总体
       * The sample is a portion of the population and should be less varied than the population       * The sample is a portion of the population and should be less varied than the population
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       * 用n-1作分母是用自由度来校正样本离差，以利于对总体参数的无偏差估计       * 用n-1作分母是用自由度来校正样本离差，以利于对总体参数的无偏差估计
       * The denominator of the sample variance is n-1, i.e., s²=SS/n-1, and the standard deviation s=√(SS/n-1).Using n-1 as the denominator is to use the degrees of freedom to correct the sample dispersion, so as to facilitate the unbiased estimation of the population parameters.       * The denominator of the sample variance is n-1, i.e., s²=SS/n-1, and the standard deviation s=√(SS/n-1).Using n-1 as the denominator is to use the degrees of freedom to correct the sample dispersion, so as to facilitate the unbiased estimation of the population parameters.
-  - 标准差 Standard deviation+ 
 +  - **标准差 Standard deviation**
       * 拇指原则：对于对称分布，均值常常在分布的中点，标准差常常在全距的1/4左右       * 拇指原则：对于对称分布，均值常常在分布的中点，标准差常常在全距的1/4左右
       * Thumb principle: For symmetrical distributions, the mean is often at the midpoint of the distribution, and the standard deviation is often about 1/4 of the full distance.       * Thumb principle: For symmetrical distributions, the mean is often at the midpoint of the distribution, and the standard deviation is often about 1/4 of the full distance.
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   * 半四分位距又叫四分差，是四分位距的一半，即SIQR=(Q3-Q1)/2   * 半四分位距又叫四分差，是四分位距的一半，即SIQR=(Q3-Q1)/2
   * 四分位距不易受极端分数的影响，适用于有不确定值的数据   * 四分位距不易受极端分数的影响，适用于有不确定值的数据
 +  * The interquartile range portrays the full range of the data in the middle 50% of the distribution, obtained by subtracting the first and third quartiles. Compared to range, the interquartile distance is less susceptible to extreme scores.
全距_标准差_四分位距.1710132003.txt.gz · 最后更改: 2024/03/11 04:40 由 fairytaleee