Standard Deviation
Definition Of Standard Deviation
The standard deviation is defined as the average amount by which individual data items in a data set differ from the arithmetic mean of all the data in the set.
The standard deviation is the square root of the variance. It is denoted by the symbol .
More About Standard Deviation
If a set of data has n values 
and if 
represents the mean of the data set, then the standard deviation is given by:
Video Examples: What is a "Standard Deviation?" and where does that formula come from
Example of Standard Deviation
If electricity bills (in dollars) of 8 houses are 70, 82, 76, 79, 83, 85, 72, 77 and mean 
is 78 then find the standard deviation.
Standard deviation
Solved Example on Standard Deviation
Ques: A survey conducted by an automobile company showed the number of cars per household and the corresponding probabilities. Find the standard deviation.
Choices:
A. 4.24
B. 0.63
C. 0.79
D. 1.9
Correct Answer: C
Solution:
Step 1: Representing the data in the table and compute X .P(X) and X2 . P(X)
Step 2: From the table, we get 
Step 3: 
Step 4: Variance 
Step 5: Variance 
Step 6: Standard deviation 
Step 7: So, the standard deviation is 0.79.