The standard deviation of a data set is based on how much each data value deviates from the mean, and is equal to the square root of the variance. The greater the dispersion of values, the larger the standard deviation. Much of statistical theory is based on the standard deviation and the 'normal' distribution.
The standard deviation is a widely used measure of variation. It is a useful measure when your data distribution is very close to a normal curve. In this situation, the mean is the best measure of central tendency, and the standard deviation is the best measure of dispersion.
In a normal distribution, if you measure 1 standard deviation to either side of the mean, you will find that 68.3% of the observations fall into this area; 95.5% of the observations fall within 2 standard deviations to either side of the mean; and 99.7% of observations fall within 3 standard deviations of the mean.
The standard deviation is calculated as follows:
Translated to English:
Let's take a look at a simple data set. The mean of the values in the 'Data Value' column is 50 (see below). Use this figure for the 'Deviation from the Mean' calculation in the next column. To better understand the process, walk through the steps of the exercise yourself.
After you understand the concept of standard deviation, you will normally use the standard deviation function on a calculator for the tedious and complex calculations. The GraphTool applet in the Tables Graphs & Charts lesson will calculate mean and standard deviation, as well as draw a graph of your own data set.
There are two versions available for the Windows95 calculator:
scientific and standard. The scientific version of the calculator
provides a method to enter your data values, then use the 's'
function to calculate the standard deviation. The calculator is
located in the Windows® accessories program group. The help
option provides the information you need to learn how to enter
numbers and use the 's' function.

Data 
Deviation 
Square of  
1 
1  50 = 
49 
 49 *  49 = 
2401  
44 
44  50 = 
6 
6 * 6 = 
36  
45 
45  50 = 
5 
5 * 5 = 
25  
46 
46  50 = 
4 
 4 *  4 = 
16  
48 
48  50 = 
2 
 2 * 2 = 
4  
48 
48  50 = 
2 
 2 *  2 = 
4  
49 
49  50 = 
1 
 1 *  1 = 
1  
50 
50  50 = 
0 
0 * 0 = 
0  
50 
50  50 = 
0 
0 * 0 = 
0  
51 
51  50 = 
1 
1 * 1 = 
1  
52 
52  50 = 
2 
2 * 2 = 
4  
52 
52  50 = 
2 
2 * 2 = 
4  
54 
54  50 = 
4 
4 * 4 = 
16  
55 
55  50 = 
5 
5 * 5 = 
25  
55 
55  50 = 
5 
5 * 5 = 
25  
100 
100  50 = 
50 
50 * 50 = 
2500  
Mean 
50  
Sum of Squares 

5062  
# of Observations  1 
(16  1) = 15  
Standard 
Square root of (5062 / 15) = 18.4 