= Solution
For the <squared discrepancy of a digit frequency>, write $d_N^2=(f_0-0.1)^2$. The plotted ordinates are $10^{-2}$, $4.00\times10^{-4}$, $1.69\times10^{-4}$, $4.90\times10^{-5}$, $3.60\times10^{-5}$ and $9.00\times10^{-6}$ in increasing $N$. Under an independent, equiprobable-digit model, the zero count is binomial and
$$
\boxed{\mathbb E[d_N^2]=\operatorname{Var}(f_0)=\frac{0.1(0.9)}N=\frac{0.09}N}.
$$
Thus the expected log-log slope is \b[$-1$]. If “relative” means division by the expected fraction before squaring, every ordinate is multiplied by 100 and the prediction becomes $9/N$; the slope is unchanged. These are nested prefixes of one digit sequence, so the points are correlated, rounded observations, not independent <variance> estimates. Their rough trend supports a reciprocal-power scale but does not prove independence or that $\pi$ is a <normal number>.
\Image[/past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2013/paper-1-digit-deviations.png]
{title=Original log-log plot of squared digit-frequency discrepancies with the independent-digit expectation}
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