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	$\mu ={\sum _{i=1}^{n}{x_{i}} \over N}$	Example
2.4.2	Skewness	$Skewness={\frac {{\sqrt {n}}\sum _{i=1}^{n}\left(x_{i}-{\overline {x}}\right)^{3}}{(\sum _{i=1}^{n}\left(x_{i}-{\overline {x}}\right)^{2})^{\frac {3}{2}}}}={\frac {{\sqrt {n}}\sum _{i=1}^{n}\left(x_{i}-{\overline {x}}\right)^{3}}{(n-1){\sqrt {n-1}}s^{3}}}$	Example
2.4.2	Mean of a sample	${\bar {x}}={\sum _{i=1}^{n}{x_{i}} \over N}$	Example
2.5.1	Range	$R=x_{L}-x_{s}$	Example
2.5.2	Sample variance	$s^{2}={\frac {1}{n-1}}\sum _{i=1}^{n}\left(x_{i}-{\overline {x}}\right)^{2}$	Example
2.5.3	Population variance	$\sigma ^{2}={\frac {1}{N}}\sum _{i=1}^{N}\left(x_{i}-\mu \right)^{2}$	Example
2.5.4	Standard deviation	$s={\sqrt {s^{2}}}={\sqrt {{\frac {1}{n-1}}\sum _{i=1}^{n}\left(x_{i}-{\overline {x}}\right)^{2}}}$	Example
2.5.5	Coefficient of variation	$C.V.={\frac {s}{\bar {x}}}$	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	$Kurtosis={\frac {\sum _{i=1}^{n}\left(x_{i}-{\overline {x}}\right)^{4}}{(\sum _{i=1}^{n}\left(x_{i}-{\overline {x}}\right)^{2})^{2}}}-3={\frac {n\sum _{i=1}^{n}\left(x_{i}-{\overline {x}}\right)^{4}}{(n-1)^{2}s^{4}}}$	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 ${\bar {x}}$= sample mean $w$=class width		Example