How to reduce the arithmetic mean and standard deviation into one indicator?

Question

Mathematics

The arithmetic mean shows the "average temperature in the hospital." Standard deviation is how two values ​​in a sample differ from each other.
If for a particular situation good dynamics is a decrease in the value in the sample, then the decreasing dynamics of the arithmetic mean indicates that the values ​​of the indicator are decreasing. The declining dynamics of the RMS suggests that the probability that the two values ​​will be very different from each other is also decreasing.
Is there a way to bring both of these stats into one?

Answer 1

Do you only have two values? Wouldn't it be better then to consider the absolute difference between them? The standard deviation does not say that you write "how two values ​​in the sample differ from each other."

Answer 2

It is possible to build M+-RMS boundaries, which will dynamically change with each of these indicators. This is most likely what you need.
You can take the derivative of mat. expectations, it will be a numerical indicator of the trend movement, so to speak. You can translate everything into relative values, then everything will be in convenient percentages or fractions. In general, set a specific task, and starting from it, you can choose what to do.