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:
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
A survey conducted by an automobile company showed the number of cars per household
and the corresponding probabilities. Find the standard deviation.
Number of cars X |
1 |
2 |
3 |
4 |
Probability P(X) |
0.32 |
0.51 |
0.12 |
0.05 |
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.
Related Terms for Standard Deviation
- Variance
- Square Root
- Arithmetic Mean
Additional Links for Standard Deviation
