Agilent Technologies InfiniiVision 3000 X-Series - Page 227

Measurements 14
Agilent InfiniiVision 3000 X-Series Oscilloscopes User's Guide 227
The following figure graphically shows the mean and standard deviation.
Standard deviation is represented by the Greek letter sigma: σ. For a
Gaussian distribution, two sigma (± 1σ) from the mean, is where 68.3
percent of the measurement results reside. Six sigma (± 3σ) 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 ith measurement result.
The standard deviation is calculated as follows:
where:
• σ = the standard deviation.
• N = the number of measurements taken.
-2σ
PHDQ
-1σ 1σ
2σ

-3σ



3σ
x
¯
=
∑
i=1
N
x
i
N
σ =
∑
i=1
N
(
x
i
− x
¯
)
2
N