how to understanf "Suppose that $\mathbf r^{(k)}$ and $\mathcal F(\mathbf r^{(k)})$ are the mean values of $\mathbf x$ and $\mathcal F(\mathbf x)$ respectively"

[ironman1996]

How to understand "Suppose that $\mathbf r^{(k)}$ and $\mathcal F(\mathbf r^{(k)})$ are the mean values of $\mathbf x$ and $\mathcal F(\mathbf x)$ respectively"?
Because $\mathbf r^{(k)}$ and $\mathcal F(\mathbf r^{(k)})$ have their meaning, they can't "suppose" to be the mean values.