It's best to think of the graphs worded this way: (and I substituted NEWER DATA for the graphs that you linked.)
IN THE EY2018 CYCLE, THESE ARE THE MONTHS IN WHICH APPLICANTS SUBMITTED THEIR APPLICATIONS:
View attachment 262174
HOWEVER< and this is very important, because applying to med school is NOT like applying to college, when you could hit that submit button at 11:30 PM on the day of the deadline and still be just fine...
read this graph to say,
"Of all application invitations, 30% went to those who submitted their app in May, 42% to those who submitted in June" etc.
See those guys (30%) who submitted in August & September? They only got 11% of the interviews.
View attachment 262175
Sorry the graphs are so big but I wanted you to be able to see them.
Take-home lesson:
1. Submit as early as you can, while still doing a quality job on your application.
2. Realize that timeliness and organization are qualities sought for in doctors, and if your application is a hot mess AND late, you are doing yourself a disservice.
3. Why doesn't submitting even earlier get me more chance at an interview?
A. You can't submit until you have your spring semester grades, so few can submit in early May.
B. Early May submissions might have lots of errors (don't rush your work).
C. Early May submissions might include some who just came out of an unsuccessful app cycle from the year before, and essentially turned in the same app with few improvements. This is not recommended.
As far as your second questions, I don't venture into meta-analysis, but I can say that these statistics are for TMDSAS applicants and do not include Texas applications to OOS med schools.