The standard deviation is used in conjunction with the mean to numerically describe distributions that are bell shaped.
The mean measures the center of the distribution, while the standard deviation measures the spread of the distribution.
Explanation:
The standard deviation is used for the purpose of measuring dispersion or the variation that occurs in the values of a data set that is taken into consideration. When the value of the standard deviation is less then this indicates that the data points lies near to the mean. When it is higher then it will be vice versa. Thus it measures the dispersion of data points with respect to the mean.
The expected value of anything can be termed as a mean. It is the thing that is acts as a center of distribution of all data points. Mean is the center of distribution whereas the standard deviation measures the dispersion of all the data points with respect to that of the mean.
