1. ANATOMY OF THE STANDARD DEVIATION
The Standard Deviation is the most used measure of dispersion (how spread out the data are from one another).
The value of the Standard Deviation tells us how closely the values of observations for a data set are clustered around the mean. A lower value of the Standard Deviation for a data set indicates that the values of that data set are spread over a relatively smaller range around the mean. A large value of the Standard Deviation for a data set indicates that the values of that data set are spread over a relatively larger range around the mean. Note below that the smaller the standard deviation, the more peaked the curve. Conversely, the larger the standard deviation, the flatter the curve becomes.
NOTATION:
When we refer to the Population Standard Deviation, it is denoted by sigma, s.
When we refer to the Sample Standard Deviation, it is denoted by a lowercase s.