Visualizing standard deviation on a Cartesian plot I came across an example where standard deviation was being plotted on a Cartesian plot (standard 2D with X and Y axes.)
This seems like a valid thing to do but in this case the example only had a single line running across the graph to "indicate" standard deviation. This to me seems not very useful, possibly dangerous and misleading. Don't you need three lines plotted to properly visualize standard deviation on a graph? Thusly:


*

*The mean

*The mean plus one standard deviation value

*The mean minus one standard deviation value


P.S. I am a software developer working on a data visualization package so please take my use of stats terminology with a grain of salt. Any corrections and feedback will be sincerely appreciated.
Rephrasing the question:
If I had a set of five data points to plot on a cartesian plane:
X:    10    20    30    35    50
Y:    20    40    5     55    10

For this sample data set (the Y values) the mean is 20 and the stdev is ~21.036 (x values plotted along the X axis and y values plotted along the Y axis.)
What would a proper plotting of the mean and the stdev on top of the X/Y data set look like?
 A: Probably a line for the mean and a line for +/- twice the standard deviation.  That would be the "default" plot for that.
That said, I think you may be missing the point of the plot with the single line for the standard deviation.  If what you're trying to represent is change in the variability of Y over X (i.e., heteroscedasticity), then a line plotting SD over X might work.  It really does depend on the data and the questions that you're trying to ask.  There just isn't a set of rules that you can follow to produce good plots every time, and in general the more automated the plotting system gets, the more useless I find it.
A: What about plotting the point with error bars, say mean +/- sd. Here's what your example data would look like:


Here's the R code I used to generate the plot:
library(ggplot2)
df = data.frame(values=c(10, 20, 30, 35, 50, 20, 40, 5, 55, 10),
  type=rep(c("X", "Y"),  each=5))

means = tapply(df$values, df$type, mean)
sds = tapply(df$values, df$type, sd)
df_summary = data.frame(means, sds, type=c("X", "Y"))

g = ggplot(data=df_summary, aes(y=means, x=type)) +
  geom_point(data=df,aes(y=values, x=type), col=2) +
  geom_errorbar(aes(ymax = means + sd, ymin=means - sd)) +
  ylab("Values")

g

