Quality Digest, March 5, 2018

Figure 11:  Eighteen Points Shifted Out into the Tails

If we now moved an additional twelve points out into the tails by placing four points at ± 1.3,

four points at ± 1.2, and four points at ± 1.1, we would have to compensate by shifting sixteen

points into the middle by placing four points at ± 0.7, six points at ± 0.8, and six points at ± 0.9 to

get the standard deviation back down to 1.005 as seen in Figure 12. The histogram in Figure 12

has a radius of gyration of 1.000, and we find percentages that match the predictions of the

empirical rule.

 

–3

–2

–1

0

1

2

3

30 moved out

66 moved in

s = 1.005

70%

96%

100%