Skip to main content
deleted 2 characters in body
Source Link
COOLSerdash
  • 31.2k
  • 10
  • 104
  • 157

It depends on how you want to define $\textit{outlier}$outlier, since there isn't one particular definition of this concept. One of the more common ways to define this, though, is to consider the region $$ [ \pi_{.25} - 1.5 \times IQR \; , \; \pi_{.75} + 1.5 \times IQR ] $$$$ [ \pi_{.25} - 1.5 \times \mathrm{IQR}\,, \; \pi_{.75} + 1.5 \times \mathrm{IQR} ] $$ where $\pi_{.25}$ and $\pi_{.75}$ are the 25th and 75th percentiles, respectively, and $IQR$$\mathrm{IQR}$ is the interquartile range, i.e. $\pi_{.75} - \pi_{.25}$. Of course, this region may be too wide or too narrow for a dataset of only 5 observations, but that is really just an inherent problem of trying to define an $\textit{outlier}$outlier from a small sample - having only 5 observations it's hard to get a feel for what the $\textit{true}$true distribution is that you are sampling from with such little information.

It depends on how you want to define $\textit{outlier}$, since there isn't one particular definition of this concept. One of the more common ways to define this, though, is to consider the region $$ [ \pi_{.25} - 1.5 \times IQR \; , \; \pi_{.75} + 1.5 \times IQR ] $$ where $\pi_{.25}$ and $\pi_{.75}$ are the 25th and 75th percentiles, respectively, and $IQR$ is the interquartile range, i.e. $\pi_{.75} - \pi_{.25}$. Of course, this region may be too wide or too narrow for a dataset of only 5 observations, but that is really just an inherent problem of trying to define an $\textit{outlier}$ from a small sample - having only 5 observations it's hard to get a feel for what the $\textit{true}$ distribution is that you are sampling from with such little information.

It depends on how you want to define outlier, since there isn't one particular definition of this concept. One of the more common ways to define this, though, is to consider the region $$ [ \pi_{.25} - 1.5 \times \mathrm{IQR}\,, \; \pi_{.75} + 1.5 \times \mathrm{IQR} ] $$ where $\pi_{.25}$ and $\pi_{.75}$ are the 25th and 75th percentiles, respectively, and $\mathrm{IQR}$ is the interquartile range, i.e. $\pi_{.75} - \pi_{.25}$. Of course, this region may be too wide or too narrow for a dataset of only 5 observations, but that is really just an inherent problem of trying to define an outlier from a small sample - having only 5 observations it's hard to get a feel for what the true distribution is that you are sampling from with such little information.

Source Link
nrussell
  • 406
  • 4
  • 8

It depends on how you want to define $\textit{outlier}$, since there isn't one particular definition of this concept. One of the more common ways to define this, though, is to consider the region $$ [ \pi_{.25} - 1.5 \times IQR \; , \; \pi_{.75} + 1.5 \times IQR ] $$ where $\pi_{.25}$ and $\pi_{.75}$ are the 25th and 75th percentiles, respectively, and $IQR$ is the interquartile range, i.e. $\pi_{.75} - \pi_{.25}$. Of course, this region may be too wide or too narrow for a dataset of only 5 observations, but that is really just an inherent problem of trying to define an $\textit{outlier}$ from a small sample - having only 5 observations it's hard to get a feel for what the $\textit{true}$ distribution is that you are sampling from with such little information.