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 alt="" />.

More about Standard Deviation

• If a set of Data has n values alt="" /> and if alt="" /> represents the Mean of the Data set, then the Standard Deviation alt="" /> is given by:

                  alt="" /> 

Example of Standard Deviation

• If electricity bills (in dollars) of 8 houses are 70, 82, 76, 79, 83, 85, 72, 77 and Mean alt="" /> is 78 then find the standard deviation.           

Standard deviation, alt="" />  

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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.

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)

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Step 2: From the table, we get alt="" />

Step 3: alt="" />              

Step 4: Variance alt="" />

Step 5: Variance alt="" />

Step 6: Standard Deviation alt="" />

Step 7: So, the Standard Deviation is 0.79.

Related Terms for Standard Deviation

• Variance
• Square Root
• Arithmetic Mean

Additional Links for Standard Deviation

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