Need for multiple values to assess variability

We usually need to make two or more measurements of a variable to get any information about its variability. A single value contains no information about the quantity's variability.

Achieving the impossible?

Fortunately, we do not need multiple sample means to assess the variability of a sample mean. Its distribution can be estimated from a single sample using

 =  μ
 = 

The distribution of the mean can be approximated with a normal distribution with this mean and standard deviation, if we replace µ and σ with and s.