Mean Plus 1 Standard Deviation. The standard normal distribution will always feature a mean value of 0 and a standard deviation value of 1. In statistics the 68 95 99 7 rule also known as the empirical rule is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two four and six standard deviations respectively.
The standard normal distribution will always feature a mean value of 0 and a standard deviation value of 1. If the observations follow a normal distribution a range covered by one standard deviation above the mean and one standard deviation below it. If the mean of a dataset is 25 and its standard deviation is 1 6 then 68 of the values in the dataset will lie between mean 1sd 25 1 6 23 4 and mean 1sd 25 1 6 26 6 99 of the values will lie between mean 3sd 25 4 8 20 2 and mean 3sd 25 4 8 29 8.
It is worth noting that there exist many different equations for calculating sample standard deviation since unlike sample mean sample standard deviation does not have any single estimator that is unbiased efficient and has a maximum likelihood.
We can expect about 68 of values to be within plus or minus 1 standard deviation. More precisely 68 27 95 45 and 99 73 of the values lie within one two and three standard deviations of the mean respectively. 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. So using the standard deviation we have a standard way of knowing what is normal and what is extra large or extra small.
