Agilent Technologies InfiniiVision 5000 Series - Page 209

Measurements and Math Functions 6
InfiniiVision Oscilloscopes User’s Guide 209
The following figure graphically shows the mean and standard deviation. Standard
deviation is represented by the Greek letter sigma: . For a Gaussian distribution, two
sigma (± 1) from the mean, is where 68.3 percent of the measurement results reside. Six
sigma (± 3) from is where 99.7 percent of the measurement results reside.
The mean is calculated as follows:
where:
x
= the mean.
N = the number of measurements taken.
x
i
= the i
th
measurement result.
The standard deviation is calculated as follows:
-2s
mean
-1s 1s
2s
68.3%
-3s
95.4%
99.7%
03s
x
x
i
i 1=
N

N
--------------=

x
i
x–
2
i 1=
N

N 1–
------------------------------=