How does variance compare to sd?

Question

Analytics

If the dispersion (range) is acceptable = 100, then sd = 10, and if 3 sigma covers almost 100% of the range, then how to understand:

3 sigma is 3 * 10 in two directions, so = 60

60 is this 99% of 100?

Answer 1

Especially for you, I generated normally distributed data with your parameters - M = 50, sd = 10.
and plotted their histogram.
As it is easy to see, these very 99.7% of the data lie in the range from 20 to 80. What did you mean when you wrote "it does not converge that 60 is 99.73%" and " that is, 60 observations in this range [20;80] is 99.73%?" - it is not clear what you had in mind, nothing fits with anything. nothing to do with the range (60) but to the percentage of the number of observations (99.73%).

Answer 2

Count the area , i.e. number of results.