The daily sunspot number is based on an average of all Wolf numbers reported during the 24h time bin of a UT day, i.e. between 0h00 and 24:00 UT. Therefore, the most logical time tag for each daily sunspot number is 12h00 UT.

The yearly average sunspot number is now obtained by taking the average of all daily numbers for the corresponding year. The result can thus be slightly different from a simple average of the 12 monthly mean values. Indeed, the months have different lengths. For years before 1849 and in particular before the 19th century, the yearly mean becomes more approximate. Indeed, when collecting past historical observations, R. Wolf had to derive monthly and yearly averages when sunspot counts were not available every day.

The smoothed monthly number results from an averaging of monthly mean values over the 13 months, from 6 months before to 6 months after a base month. All months are weighted equal except for the extreme ones, which are weighted by 1/2. This is expressed by the formula:
Rs= (0.5 Rm-6 + Rm-5 + Rm-4 + Rm-3 + Rm-2 + Rm-1 + Rm + Rm+1 + Rm+2 + Rm+3 + Rm+4 + Rm+5 + 0.5 Rm+6 ) / 12
In signal processing jargon, this would be called a "tapered box-car" smoothing function.

Until 1980, traditionally, the sunspot number was essentially the Wolf number provided by the Zürich observatory, with some cross-validation relative to a network of supporting stations.

Other sunspot numbers, like the Boulder sunspot number or Wolf numbers provided by individual stations, are often 20 to 50% higher than the International Sunspot Number. You may thus wonder if anything is wrong with either data set. In fact, this difference is easy to understand and find its roots in the past origins of the sunpot number.

Indeed, at the level of a single observation by a single observer, there is inevitably a degree of subjectivity. However, as sunspots are simple well-defined features, the range of subjectivity remains limited. The rms dispersion between simultaneous daily observations by many separate observers is about 8%. Part of this dispersion is also due to random variations in local conditions (weather, seeing), indicating that the actual impact of human subjectivity is even lower.

Indeed, nowadays, we can observe the Sun in many different and sophisticated ways: CCD imaging, spectrocopy, space probes, radioastronomy. These techniques allow to probe our star in various quantitative ways. However, they were created only over the past few decades. Many modern instruments are also unique and have a limited lifetime (spacecrafts). Therefore, the associated data sets are limited to just one or a few solar activity cycles, i.e. a duration that is too short to study the secular variability of this cycle.

Since July 2015, there are sunspot number values between 0 and 11, although by definition the minimum non-null Wolf number is 11 ( 1 group = 10 + 1 spot = 1 , making a grand total of 11). How come there are data with values between 0 and 11?