3.0.2 简单的数据汇总
library(ISLR)
summary(Auto)
## mpg cylinders displacement horsepower weight
## Min. : 9.00 Min. :3.000 Min. : 68.0 Min. : 46.0 Min. :1613
## 1st Qu.:17.00 1st Qu.:4.000 1st Qu.:105.0 1st Qu.: 75.0 1st Qu.:2225
## Median :22.75 Median :4.000 Median :151.0 Median : 93.5 Median :2804
## Mean :23.45 Mean :5.472 Mean :194.4 Mean :104.5 Mean :2978
## 3rd Qu.:29.00 3rd Qu.:8.000 3rd Qu.:275.8 3rd Qu.:126.0 3rd Qu.:3615
## Max. :46.60 Max. :8.000 Max. :455.0 Max. :230.0 Max. :5140
##
## acceleration year origin name
## Min. : 8.00 Min. :70.00 Min. :1.000 amc matador : 5
## 1st Qu.:13.78 1st Qu.:73.00 1st Qu.:1.000 ford pinto : 5
## Median :15.50 Median :76.00 Median :1.000 toyota corolla : 5
## Mean :15.54 Mean :75.98 Mean :1.577 amc gremlin : 4
## 3rd Qu.:17.02 3rd Qu.:79.00 3rd Qu.:2.000 amc hornet : 4
## Max. :24.80 Max. :82.00 Max. :3.000 chevrolet chevette: 4
## (Other) :365
mean(Auto$mpg)
## [1] 23.44592
样本平均值的计算：\[\bar{Y}=\frac{1}{n}\sum\limits_{i=1}^ny_i\]
样本的方差：\[s^2=\frac{1}{n-1}\sum\limits_{i=1}^n(x_i-\bar{x})^2\]
线性相关系数：\[r=\frac{\sum\limits_{i=1}^n(x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum\limits_{i=1}^n(x_i-\bar{x})^2}\sqrt{\sum\limits_{i=1}^n(y_i-\bar{y})^2}}\]
课堂练习：
统计7位同学周未的学习时间，数据为：8，11，7，13，9，5，9，计算同学学习时间的均值，中位数、四分位数、标准差和极差（使用手算）。
\(\bar{x}=\frac{8+11+7+13+9+5+9}{7}=8.85\)
\(s^2=\frac{(8-8.85)^2+\cdots+(9-8.85)^2}{7-1}=6.81\)
\(s=\sqrt{s^2}=\sqrt{6.81}=2.6\)
Median = 9; Mode = 9; Range = Max - min = 13-5=8
d <- c(8,11,7,13,9,5,9)
mean(d)
## [1] 8.857143
median(d)
## [1] 9
mode(d)
## [1] "numeric"
quantile(d)
## 0% 25% 50% 75% 100%
## 5.0 7.5 9.0 10.0 13.0
sd(d)
## [1] 2.609506