Apply function to each column in a data frame observing each columns existing data type

If it were an "ordered factor" things would be different. Which is not to say I like "ordered factors", I don't, only to say that some relationships are defined for 'ordered factors' that are not defined for "factors". Factors are thought of as ordinary categorical variables. You are seeing the natural sort order of factors which is alphabetical lexical order for your locale. If you want to get an automatic coercion to "numeric" for every column, ... dates and factors and all, then try:

sapply(df, function(x) max(as.numeric(x)) )   # not generally a useful result

Or if you want to test for factors first and return as you expect then:

sapply( df, function(x) if("factor" %in% class(x) ) { 
            max(as.numeric(as.character(x)))
            } else { max(x) } )

@Darrens comment does work better:

 sapply(df, function(x) max(as.character(x)) )  

max does succeed with character vectors.

The reason that max works with apply is that apply is coercing your data frame to a matrix first, and a matrix can only hold one data type. So you end up with a matrix of characters. sapply is just a wrapper for lapply, so it is not surprising that both yield the same error.

The default behavior when you create a data frame is for categorical columns to be stored as factors. Unless you specify that it is an ordered factor, operations like max and min will be undefined, since R is assuming that you've created an unordered factor.

You can change this behavior by specifying options(stringsAsFactors = FALSE), which will change the default for the entire session, or you can pass stringsAsFactors = FALSE in the data.frame() construction call itself. Note that this just means that min and max will assume "alphabetical" ordering by default.

Or you can manually specify an ordering for each factor, although I doubt that's what you want to do.

Regardless, sapply will generally yield an atomic vector, which will entail converting everything to characters in many cases. One way around this is as follows:

#Some test data
d <- data.frame(v1 = runif(10), v2 = letters[1:10], 
                v3 = rnorm(10), v4 = LETTERS[1:10],stringsAsFactors = TRUE)

d[4,] <- NA

#Similar function to DWin's answer          
fun <- function(x){
    if(is.numeric(x)){max(x,na.rm = 1)}
    else{max(as.character(x),na.rm=1)}
}   

#Use colwise from plyr package
colwise(fun)(d)
         v1 v2       v3 v4
1 0.8478983  j 1.999435  J

If you want to learn your data summary (df) provides the min, 1st quantile, median and mean, 3rd quantile and max of numerical columns and the frequency of the top levels of the factor columns.