### 4.1 The overall activity level

Here we consider the ^{14}C-based decade reconstruction of sunspot numbers (shown in Figure 17). It is
identical to that shown in Figure 14, but includes also a Gleissberg 1-2-2-2-1 filter in order to suppress noise
and short-term fluctuations. This series forms the basis for the forthcoming analysis, while differences
related to the use of other reconstructions are discussed.
First, we analyze the distribution of the occurrence frequency of sunspot-number values. The histogram
for sunspot-number distribution (for the series shown in Figure 17) is shown in Figure 18. The
over-decades filtered sunspot numbers range between 0 and 95. The bulk of the distribution can be roughly
approximated by a normal Gaussian distribution with a mean of 31 and standard deviation of = 30.
However, there are apparent excesses both at very low (SN < 10) and high (SN > 70) sunspot numbers.
These excesses are very unlikely to be a result of random fluctuations or noise in the data and, as argued in
Section 4.3, correspond to special states of the solar dynamo, namely, the grand minima and grand
maxima. It is important that the entire distribution is more-or-less consistent with the directly-observed
sunspot series after 1610, suggesting that the latter can serve as a representative sample for
sunspot-activity statistics, including a grand minimum (the Maunder minimum) and the modern
maximum.