11.4 Inversion about the mean

Suppose I have four data points and their mean:

data = [3, 1, 2, 5]
mean = float(sum(data)) / len(data)
mean

2.75

I show these values in the bar chart on the left-hand side of Figure 11.6.

Figure 11.6: Inversion about the mean for four data points

On the right-hand side, I’ve inverted the data about the mean. Geometrically, if a value x is above the mean with difference d from the mean, the inverted value is the mean minus |d|. Look at the fourth bar. The value is well above the mean. The inverted value on the right is below the mean by the same amount.

I cover inversion about the mean in section 9.6.2 of Dancing with Qubits. [DWQ]

For a value below the mean, again look at the difference d from the mean. The inverted value is the mean plus |d|. The second bar is a good example of this. Given a ...