To breakdown data by day of the month, you can use Mixpanel's JQL (JavaScript Query Language) built-in function mixpanel.numeric_bucket(). This function can be used to segment events over a calendar period when applied to the time property.
Here is an example of how you can use it:
```
function main() {
return Events({
from_date: "2016-01-01",
to_date: "2016-01-30",
}).groupBy([mixpanel.numeric_bucket('time', {bucket_size: 86400 ** 1000})],
mixpanel.reducer.count());
}
In this example, `86400 ** 1000` is used as the bucket size to represent one day in milliseconds.
However, to specifically breakdown data into two segments: 1st 11 days vs the rest of the month, you might need to write a custom function in JQL to bucket the days accordingly. Unfortunately, the provided knowledge sources do not include a specific example of how to do this.
For more details, you can refer to the [Mixpanel documentation on JQL](https://docs.mixpanel.com/docs/reports/apps/jql#mixpanelnumeric_bucket).