Can a categorical variable be an outlier?
Ex...If students in a class was asked what color their hair color was and most said brown or blonde but one replied white is this person considered an outlier?
Is this class at a Nursing home?
Probably white is an outlier for the intents of your understanding. Later in life, you will find it in the norm.
No, a categorical variable cannot be considered an outlier in the traditional statistical sense. Outliers are typically associated with numerical variables and are defined as data points that deviate significantly from the overall pattern. Categorical variables, on the other hand, represent qualitative attributes or characteristics that are not measured on a numerical scale.
In your example, the person who responded with "white" hair color can be seen as an unusual or uncommon response, but they would not be considered an outlier in the statistical sense. Instead, their response would simply be a different category within the variable.
To determine whether a response is considered an outlier, you would typically look at numerical variables and analyze the distribution of data using methods such as box plots or calculating z-scores. Categorical variables, such as hair color in this case, do not have a numerical scale to measure deviations from, so the concept of outliers does not apply.