Standard errors and CIs from formulae
If a formula can be found for the standard error of an estimator, an approximate 95% confidence interval can be found from
estimate - 2 s.e. to estimate + 2 s.e.
For some estimators, there is no formula for the standard error, so a different approach is needed.
Rainfall example
Understanding of the distribution of rainfall lets farmers make better choices about the crops that are grown and when they are planted, especially in areas prone to drought. A useful summary is the upper quartile of the rainfall distribution in a month — the rainfall that is exceeded in only 1 out of 4 years.
The diagram below shows October rainfall in Samaru, Nigeria for the 56 years between 1928 and 1983.
Assuming that there is no climate change, the sample upper quartile is our best point estimate of the upper quartile for the underlying population distribution, but there is no convenient formulae for its standard error.