生物统计学学习笔记描述性统计变量.docx

生物统计学学习笔记（1） 描述性统计Descriptive Statistics 位置测度法 measure of location One type of measure useful for summarizing data defines the center, or middle, of the sample. This type of measure is a measure of location. 算术平均数：arithmetic mean The arithmetic mean is the sum of all the observations divided by the number of observations. It is written in statistical terms as 算术平均是的缺点是对极端是太敏感了。在这种情况下他不能代表样本的绝大多数。 The arithmetic mean is, in general, a very natural measure of location. One of its main limitations, however, is that it is oversensitive to extreme values. In this instance, it may not be representative of the location of the great majority of sample points. 中位数 median Suppose there are n observations in a sample. If these observations are ordered from smallest to largest, then the median is defined as follows: 1. The（ n+12）th largest observation if n is odd 2. The average of the（ n2）th and （ n2+1）th largest observations if n is even 众数mode The mode is the most frequently occurring value among all the observations in a sample. 几何平均数The Geometric Mean The geometric mean is the antilogarithm of log x, where 离散性测度 Measure s of Spread 极差range 一个样本中最大值和最小值之间的差异 The range is the difference between the largest and smallest observations in a sample 分位数 The pth percentile is defined by (1) The (k + 1)th largest sample point if np/100 is not an integer (where k is the largest integer less than np/100). (2) The average of the (np/100)th and (np/100 ??1)th largest observations if np/100 is an integer. Percentiles are also sometimes called quantiles. R可以如下求解 quantile(pzcz$BornAlive) 0% 25% 50% 75% 100% 0 8 10 12 20 quantile(pzcz$BornAlive,probs=c(0.1,0.9),na.rm = TRUE,type = 2) 10% 90% 6 13 quantile(pzcz$BornAlive,probs=c(0.1,0.25,0.5,0.75,0.9),na.rm = TRUE,type = 2) 10% 25% 50% 75% 90% 6 8 10 12 13 方差与标准差The Variance and Standard Deviation The sample variance, or variance, is defined as follows: S2=i=1n(xi-x)n-1 A rationale for using n ? 1 in the de