If you want to show how precisely you have determined the mean: Of course, if you do decide to show SD error bars, be sure to say so in the figure legend so no one will think it is a SEM. I see no advantage to plotting a mean and SD rather than a column scatter graph, box-and-wiskers plot, or a frequency distribution. A graph showing mean and SD error bar is less informative than any of the other alternatives, but takes no less space and is no easier to interpret. But a SD is only one value, so is a pretty limited way to show variation. What about plotting mean and SD? The SD does quantify variability, so this is indeed one way to graph variability. Alternatives are to show a box-and-whiskers plot, a frequency distribution (histogram), or a cumulative frequency distribution. What better way to show the variation among values than to show every value? If your data set has more than 100 or so values, a scatter plot becomes messy. With fewer than 100 or so values, create a scatter plot that shows every value. Even if each value represents a different lab experiment, it often makes sense to show the variation. If each value represents a different individual, you probably want to show the variation among values. If you want to show the variation in your data: There are better alternatives to graphing the mean with SD or SEM.
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