The PMI series fit quite well with other economic data. Markit releases preliminary PMIs on 24th of the month for that month. They are sometimes revised when more data become available, but the revisions aren't usually too big.
The September PMI for China rose a little, extending the rise which began in August. Looks to me that Chinese growth has bottomed.
Disclaimer. After nearly 40 years managing money for some of the largest life offices and investment managers in the world, I think I have something to offer. These days I'm retired, and I can't by law give you advice. I do make mistakes, but I try hard to do my analysis thoroughly, and to make sure my data are correct. Remember: the unexpected sometimes happens. The expected does too, but all too often it takes longer than you thought it would.
The Goddess of Markets punishes (eventually) greed, folly, laziness and arrogance. No matter how many years you've served Her. Take care. Be humble. And don't blame me.
BTW, clicking on most charts will produce the original-sized, i.e., bigger version.