When we plot the mean of a variable on a scatter plot or a bar plot, why do we plot the standard error of the mean in both directions: positive and negative?
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Best Answer
Because your estimated mean might differ from the true mean in either direction: it can be too high or it can be too low.
If you estimate the mean from your sample to be (e.g.) 3 and you also know that standard error (loosely speaking the average deviation of the estimate from the true mean) is 2 then you expect that your estimate might be off by about 2 in either direction.
In such a case when you see your estimate as "3" there is a reasonable chance it was "1" (as 3 is within a standard error of 1) and as high as "5" (as 3 is within a standard error of 5).