Based on your example e.g. 16 files for 10:25, i.e. 010.csv, 011.csv, 012.csv, etc. Under the assumption that your naming convention follows the order of the files in the directory, you could try:
csvFiles <- list.files(pattern="\\.csv")[10:15]#here [10:15] ... in production use your function parameter here
file_list <- vector('list', length=length(csvFiles))
df_list <- lapply(X=csvFiles, read.csv, header=TRUE)
names(df_list) <- csvFiles #OPTIONAL: if you want to rename (later rows) to the csv list
df <- do.call("rbind", df_list)
mean(df[ ,"columnName"])
These code snippets should be possible to pimp and incorprate into your routine.