1. Standard Deviation
Tutorial

2. Topics
Definition
Formula
Examples
Transaction Details

3. Definition
Standard deviation is a statistical measure of spread or variability.
The standard deviation is the root mean square (RMS) deviation of the values from their arithmetic mean.
standard deviation shows how much variation exists from the average .
A low standard deviation indicates that the data points tend to be very close to the mean
High standard deviation indicates that the data points are spread out over a large range of values.

4. Formula

5. Formula (Continued)
where Σ = Sum of               X = Individual score               M = Mean of all scores               N = Sample size (Number of scores)
s = square root of[(sum of Xsquared -((sum of X)*(sum of X)/N))/(N-1)]

6. Example
To find the Standard deviation of 1,2,3,4,5.   Step 1: First, square each of the scores. X X2 1 2 4 3 9 16 5 25

7. Example (Continued) Step2: Use the formula
            s = square root of[(sum of Xsquared -((sum of X)*(sum of X)/N))/(N-1)]
            = square root of[(55-((15)*(15)/5))/(5-1)]             = square root of[(55-(225/5))/4]             = square root of[(55-45)/4]             = square root of[10/4]             = square root of[2.5]             s =

8. Transaction Details Following data elements are capture:
Min
Max
Average
Standard Deviation
Initiated Count
Completed Count
Failure Percentage
Transaction Rate/Sec (TPS)
Standard Deviation gives the true picture of variation in response time.

9. Transaction Details – Example1
eg. Login Page
Duration 1
0.929 2
3.779 3
0.524 4
3.987 5
1.412 6
0.222 7
2.603 8
1.139 9
2.187 10
0.499
Average µ
1.728
Stand-Dev. σ
1.3580

10. Transaction Details – Example2
eg. Login Page
Duration 1
0.979 2
1.001 3
1.021 4
0.987 5
1.012 6
0.922 7
1.203 8
1.139 9
1.187 10
0.999
Average µ
1.045
Stand-Dev. σ
0.095