Biostatistics with R/Descriptive Statistics

Summary For Formular with R

Formula Number	Name	Formula	Formula with R
2.3.1	Class interval width using Sturges’s Rule	$w=\frac{R}{k}$	Example
2.4.1	Mean of a population	$\mu =\frac{\sum _{i=1}^n{x}_i}{N}$	Example
2.4.2	Skewness	$Skewness=\frac{\sqrt{n}\sum _{i=1}^n{(x_i-\bar{x})}^3}{(\sum _{i=1}^n{(x_i-\bar{x})}^2{)}^{\frac{3}{2}}}=\frac{\sqrt{n}\sum _{i=1}^n{(x_i-\bar{x})}^3}{(n-1)\sqrt{n-1}{s}^3}$	Example
2.4.2	Mean of a sample	$\overline{x}=\frac{\sum _{i=1}^n{x}_i}{N}$	Example
2.5.1	Range	$R=x_L-x_s$	Example
2.5.2	Sample variance	$s^2=\frac{1}{n-1}\sum _{i=1}^n{(x_i-\bar{x})}^2$	Example
2.5.3	Population variance	${\sigma }^2=\frac{1}{N}\sum _{i=1}^N{(x_i-\mu )}^2$	Example
2.5.4	Standard deviation	$s=\sqrt{s^2}=\sqrt{\frac{1}{n-1}\sum _{i=1}^n{(x_i-\bar{x})}^2}$	Example
2.5.5	Coefficient of variation	$C.V.=\frac{s}{\overline{x}}$	Example
2.5.6	Quartile location in ordered array	$Q_1=\frac{1}{4}(n+1)$	Example
2.5.7	Interquartile range	$IQR=Q_3-Q_1$	Example
2.5.8	Kurtosis	$Kurtosis=\frac{\sum _{i=1}^n{(x_i-\bar{x})}^4}{(\sum _{i=1}^n{(x_i-\bar{x})}^2{)}^2}-3=\frac{n\sum _{i=1}^n{(x_i-\bar{x})}^4}{(n-1{)}^2{s}^4}$	Example
Symbol Key	$C.V.$= coefficient of variation $IQR$ = Interquartile range $k$ = number of class intervals $m$ = population mean $N$ = population size $n$ = sample size $(n-1)$=degrees of freedom $Q_1$ = first quartile $Q_2$= second quartile = median $Q_3$= third quartile $R$ =range $s$ =standard deviation $s^2$= sample variance ${\sigma }^2$= population variance $x_i$=$i^{t}h$ data observation $x_L$= largest data point $x_S$=smallest data point $\overline{x}$= sample mean $w$=class width		Example