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## Your original data is already the result of table().
## Here are two versions, one using barchart and one barplot.
tmpc <- textConnection("
Month      Core(%)   Non_core(%)
1             45                55
2             48                52
3             36                64
4             60                40
5             35                65
")
tmp <- data.matrix(read.table(tmpc, header=TRUE,
row.names="Month"))
close(tmpc)
barchart(tmp, horizontal=FALSE)
barplot(t(tmp))