R语言实战 - 高级数据管理（1）

1. 一个数据处理难题

a. 确定一个单一的成绩衡量指标

b. 前20%的学生评定为A，接下来20%评定为B，以此类推

c. 按字母顺序对学生排序

2. 数值和字符处理函数

数值函数（数学，统计，概率）

字符处理函数

2.1 数学函数

> abs(-4)
[1] 4
> 
> sqrt(25)
[1] 5
> 
> ceiling(3.475)
[1] 4
> 
> floor(3.475)
[1] 3
> 
> trunc(5.99)
[1] 5
> 
> round(3.475, digits=2)
[1] 3.48
> 
> signif(3.475, digits=2)
[1] 3.5
> 
> cos(3.1415926)
[1] -1
> 
> sin(3.1415926)
[1] 5.358979e-08
> 
> acos(-0.416)
[1] 1.999839
> 
> sinh(2)
[1] 3.62686
> 
> asinh(3.627)
[1] 2.000037
> 
> log(10)
[1] 2.302585
> 
> log10(10)
[1] 1
> 
> exp(2.3026)
[1] 10.00015
> 

2.2 统计函数

> mean(c(1, 2, 3, 4))
[1] 2.5
> 
> median(c(1, 2, 3, 4))
[1] 2.5
> 
> sd(c(1, 2, 3, 4))
[1] 1.290994
> 
> var(c(1, 2, 3, 4))
[1] 1.666667
> 
> mad(c(1, 2, 3, 4))
[1] 1.4826
> 
> x <- c(1, 2, 3, 4)
> y <- quantile(x, c(.3, .84))
> y
 30%  84% 
1.90 3.52 
> 
> range(x)
[1] 1 4
> 
> diff(range(x))
[1] 3
> 
> sum(x)
[1] 10
> 
> x <- c(1, 5, 23, 29)
> diff(x)
[1]  4 18  6
> 
> min(x)
[1] 1
> 
> max(x)
[1] 29
> 
> scale(x, center=TRUE, scale=TRUE)
           [,1]
[1,] -0.9925397
[2,] -0.6984539
[3,]  0.6249324
[4,]  1.0660612
attr(,"scaled:center")
[1] 14.5
attr(,"scaled:scale")
[1] 13.60147
> 

> x <- c(1, 2, 3, 4, 5, 6, 7, 8)
> mean(x)
[1] 4.5
> sd(x)
[1] 2.44949
> 
> n <- length(x)
> meanx <- sum(x)/n
> css <- sum((x - meanx)^2)
> sdx <- sqrt(css / (n-1))
> meanx
[1] 4.5
> sdx
[1] 2.44949
> 

2.3 概率函数

> x <- pretty(c(-3, 3), 30)
> x
 [1] -3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 -1.0 -0.8 -0.6 -0.4 -0.2
[16]  0.0  0.2  0.4  0.6  0.8  1.0  1.2  1.4  1.6  1.8  2.0  2.2  2.4  2.6  2.8
[31]  3.0
> y <- dnorm(x)
> y
 [1] 0.004431848 0.007915452 0.013582969 0.022394530 0.035474593 0.053990967
 [7] 0.078950158 0.110920835 0.149727466 0.194186055 0.241970725 0.289691553
[13] 0.333224603 0.368270140 0.391042694 0.398942280 0.391042694 0.368270140
[19] 0.333224603 0.289691553 0.241970725 0.194186055 0.149727466 0.110920835
[25] 0.078950158 0.053990967 0.035474593 0.022394530 0.013582969 0.007915452
[31] 0.004431848
> plot(x, y, type="l", xlab="NormalDeviate", ylab="Density", yaxs="i")
> 

> pnorm(1.96)
[1] 0.9750021
> qnorm(.9, mean=500, sd=100)
[1] 628.1552
> rnorm(50, mean=50, sd=10)
 [1] 67.26521 54.63231 42.90968 48.38989 73.67308 49.74476 57.81742 67.75197
 [9] 66.51772 48.48707 39.37449 35.09612 59.43735 58.02651 40.43783 51.18190
[17] 63.75237 39.67564 42.67555 50.88800 43.47265 58.69022 64.55702 34.35042
[25] 63.23016 45.81644 43.31544 54.58287 50.46310 31.72297 40.34214 55.06260
[33] 42.25432 45.63078 56.23651 53.27949 47.83063 53.69351 56.68358 46.04020
[41] 57.20872 52.52052 49.20011 47.71317 55.79194 42.20664 48.22365 43.57350
[49] 33.02280 36.45630
> 

2.3.1 设定随机数种子

> runif(5)
[1] 0.8650632 0.2548104 0.7736314 0.9595250 0.5731663
> runif(5)
[1] 0.3458971 0.8683841 0.7487097 0.1382841 0.1953431
> set.seed(1234)
> runif(5)
[1] 0.1137034 0.6222994 0.6092747 0.6233794 0.8609154
> set.seed(1234)
> runif(5)
[1] 0.1137034 0.6222994 0.6092747 0.6233794 0.8609154
> 

2.3.2 生成多元正态数据

> library(MASS)
> options(digits=3)
# 生成随机数种子
> set.seed(1234)
# 指定均值向量、协方差阵
> mean <- c(230.7, 146.7, 3.6)
> sigma <- matrix(c(15360.8, 6721.2, -47.1,
+                    6721.2, 4700.9, -16.5,
+                     -47.1,  -16.5,   0.3), nrow=3, ncol=3)
# 生成500个伪随机观测数据
> mydata <- mvrnorm(500, mean, sigma)
# 为方便，结果从矩阵转换为数据框
> mydata <- as.data.frame(mydata)
# 为变量指定了名称
> names(mydata) <- c("y", "x1", "x2")
# 确认拥有500个观测和3个变量
> dim(mydata)
[1] 500   3
# 输出前10个观测
> head(mydata, n=10)
       y    x1   x2
1   98.8  41.3 3.43
2  244.5 205.2 3.80
3  375.7 186.7 2.51
4  -59.2  11.2 4.71
5  313.0 111.0 3.45
6  288.8 185.1 2.72
7  134.8 165.0 4.39
8  171.7  97.4 3.64
9  167.2 101.0 3.50
10 121.1  94.5 4.10
> 

2.4 字符处理函数