I'm not really clear on what you want here. Are you talking about plotting 
multiple data points for each value ?   In that case something like  boxplot 
might be what you want. Otherwise if you just wish to plot a data point for 
each occurance of Normal etc then this will work but I'm not sure how 
appropriate it is as a way to look at the data.

If the graph looks a bit squashed, just stretch it.  


x  <- '"Measured"      "Eyeball"
46.5   Normal
43.5   Mild
56.2   Normal
41.1   Mild
37.8   Moderate
12.6   Severe
17.3   Moderate
39.1   Normal
26.7   Mild
NA     Normal
27.9   NA
68.1   Normal'

xx <- read.table(textConnection(x), header=TRUE, as.is=TRUE); xx

df1 <- data.frame(Eyeball= c("Normal", "Mild", "Moderate", "Severe"),
                   nums= c(1:4))
                   
df2 <- merge(xx, df1, by="Eyeball", all=TRUE)

plot(df2[,2], xaxt="n", xlab="Eyeball", ylab="Measured")
mtext(1, text=df2[,1], at=1:length(df2[,1]), line = 1 , cex=.7  )



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