On average, a bright comet appears about once each decade. Statistically, this means that a. one will definitely be observed every tenth year. b. one will definitely be observed in each 10 -year period. c. exactly 10 comets will be observed in a century. d. about 10 comets will be observed in a century.

In astronomy, statistics play a crucial role in making sense of observational data. When we say a comet appears once every decade 'on average', we're using statistical measures to describe patterns observed over long periods. This doesn't mean that we can predict the exact year a comet will appear. Rather, it means that over many decades, the comets' occurrences average out to one per ten years.
Understanding statistical terms like 'average' helps us interpret data correctly. In this case, an average rate of one comet per decade doesn’t guarantee a comet will appear every tenth year.

• It’s like tossing a coin; each result is random, but over many tosses, you'd expect about half to come up heads.
• Similarly, while some decades might see no comets and others might see two, the long-term average will still align with the expected rate.

The concept of an 'average rate' is straightforward yet vital. When astronomers note that a bright comet appears roughly once every decade, they are referring to the average rate over a long time frame. It’s important to distinguish between 'on average' and 'definitely'.
'Average rate' doesn't imply certainty for specific periods. Instead, it is a statistical measure reflecting the typical frequency of an event over an extended period. For example, if we say the average rainfall in a region is 1000 mm per year, some years might see more and others less, but over many years, it averages to that number.
Similarly, for comet appearances:

• One comet every decade on average means that over a century, you would expect approximately 10 comets.
• This approximation helps astronomers predict patterns without expecting exact annual occurrences.

When discussing comet appearances, it's essential to understand both the predictability and randomness of such events. Comets are celestial objects with highly variable orbits, making their visits infrequent and unpredictable.
Yet, thanks to historical observations, we can estimate their average appearance rates. The statement that a bright comet appears once every decade is based on observed data and helps us form expectations. However, this rate is an average:

• Comets don’t adhere to a rigid schedule.
• Some decades may see multiple comets, while others may have none.

In summary, understanding the average rate of comet appearances aids in managing expectations and appreciating the patterns within our solar system. Even if we cannot predict the exact timing, astronomers can confidently assert that over a century, about ten comets can be expected to grace our skies.