Which usage is correct?
This is shown in/on the forecast.
The numbers are in/on the forecast.
You would usually use "in the forecast"
"In the forecast" means that the forecast has predicted some results(/outcome/event) and you are talking about what the results are.
The only time you might use "on the forecast" is if you meant "the forecast" to be a TV show or other media. For example, if you had watched the weather forecast on TV, you might say "I saw on the (weather) forecast that it will rain".
This is a similar construct to other TV shows: "I saw it on Eastenders yesterday" but using "the forecast" to mean a specific TV show or segment of a TV show with revolves solely around a forecast of some type.