Download Anatomy: Standard Deviation

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.
Mean = 120
Standard Deviation = 2
n = 500
Mean = 120
60
Standard Deviation = 20
n = 500
80
70
50
Frequency
Frequency
60
40
30
20
50
40
30
20
10
10
0
0
112
117
122
127
80
NOTATION:
When we refer to the Population Standard Deviation, it is denoted by sigma,
130
s.
When we refer to the Sample Standard Deviation, it is denoted by a lowercase s.
180