I submitted a paper to the journal with a homepage statement that reads, '7 days from submission to first decision (median).'" After one month it’s “Editor assigned “. What does this means? What is the meaning of 7 in this situation? Thank you.
If a journal desk rejects a lot of submissions without sending them to reviewers, the statistics, especially the median are heavily skewed toward "early" decisions even if the mean time or even, perhaps, the modal time is quite long.
The above can be the case if the journal gets a lot of inappropriate submissions: out of scope, cranks, etc.
And, you probably won't be notified that you haven't been desk rejected and it may take a while for the editor to find and get agreement from reviewers. This implies a stretch between the desk decision and the next one about which you would be notified.
In that case, what it means is that if you don't get a decision in a week (7 days) you will likely need to wait a while for that first decision other than desk reject.
The distribution is neither uniform nor normal.
My impression is that these stats are rather meaningless and mostly serve as a bait.
I submitted a paper to a journal advertising 6 weeks median to first decision and 8 weeks to publication. The first review took 6.5 months (I wrote to the Editor after 6 months to chase it up), the second review is going on for 3+ months now.