Mean Plus Two Standard Deviations. Hence one can interpret the value of the standard deviation by reference to the normal curve. We can do the same with any number of other distributions.
To compute the probability that an observation is within two standard deviations of the mean small differences due to rounding. It will always be between 0 and 25 outside two standard deviations from the mean and for continuous unimodal densities i think the bounds are 0 to 11 1 1 9 outside two standard deviations from the mean. Consequently if we know the mean and standard deviation of a set of observations we can obtain some useful information by simple arithmetic.
Because standard deviation is a measure of variability about the mean this is shown as the mean plus or minus one or two standard deviations.
Consequently if we know the mean and standard deviation of a set of observations we can obtain some useful information by simple arithmetic. Hence one can interpret the value of the standard deviation by reference to the normal curve. Pr μ 2 σ x μ 2 σ φ 2 φ 2 0 9772 1 0 9772 0 9545 displaystyle pr mu 2 sigma leq x leq mu 2 sigma phi 2 phi 2 approx 0 9772 1 0 9772 approx 0 9545. Consequently if we know the mean and standard deviation of a set of observations we can obtain some useful information by simple arithmetic.