# When reporting mean values should the standard error be included?

I'm trying to understand when to report the standard error.

When reporting results in a scientific paper or essay, should any mean values also have the standard error reported alongside?

For example, let's say you measure the amount of toys a child buys each week over a year. You decide to calculate monthly averages. Should you also calculate the standard error and report this alongside?

Such as "In January the monthly mean of toys bought were 4 (+/- 0.7)"

# Example Dataset

Toys Bought each week
Week 1: 4
Week 2: 3
Week 3: 4
Week 4: 1
Monthly average: 3
Standard Deviation: 1.41421
Standard Error: 0.707106781187


## Summary Question

Should you always report the standard error when reporting a mean value, or is the standard error only applicable to certain things?

• I think you meant standard deviation – rep_ho Oct 8 '16 at 16:18

I would recommend including a confidence interval when reporting means instead of the standard error. The confidence interval of a mean is its standard error multiplied by a critical $t$ value. This lends itself to more useful interpretation in most cases. Read more about interpreting confidence intervals in the following article: