Fluke Digital Multimeter - Impact of Sample Size and Automation; Effect of Sample Size on Uncertainty

©Fluke Calibration 2011 Basics Of Measurement Uncertainty for DMM Calibration 58
What if more measurements were taken, does
that improve the uncertainty?
Increased degrees of freedom
V
eff
= 5 10, 20 or 100
Causes marginal improvements
in k and in
• 5 measurements, V
eff
= 5.2
− k = 2.57, = 31 mA
• 9 measurements, V
eff
= 10.3
− k = 2.23, = 27 mA (4 mA better)
• 17 measurements, V
eff
= 20.7
− k = 2.09, = 25 mA (2 mA better)
• 78 measurements, V
eff
= 100.9
− k = 1.984, = 24 mA (1 mA better)
Fraction p in percent
Degrees of
freedom 
68.27 90 95 95.45 99 99.73
1 1.84 6.31 12.71 13.97 63.66 235.8
2 1.32 2.92 4.3 4.53 9.92 19.21
3 1.2 2.35 3.18 3.31 5.84 9.22
4 1.14 2.13 2.78 2.87 4.6 6.62
5 1.11 2.02 2.57 2.65 4.03 5.51
6 1.09 1.94 2.45 2.52 3.71 4.9
7 1.08 1.89 2.36 2.43 3.5 4.53
8 1.07 1.86 2.31 2.37 3.36 4.28
9 1.06 1.83 2.26 2.32 3.25 4.09
10 1.05 1.81 2.23 2.28 3.17 3.96
20 1.03 1.72 2.09 2.13 2.85 3.42
50 1.01 1.68 2.01 2.05 2.68 3.16
100 1.005 1.66 1.984 2.025 2.626 3.077

1 1.645 1.96 2 2.576 3
U
m
U
m
U
m
U
m
U
m
So improves only 7 mA by taking
73 more measurements
U
m