Do people who date get married faster?

Q: A lot of people say that when a girl decides not to date boys and rather to wait until a boy comes and proposes for her in the right way, then often she will end up waiting very very long until she is married. And that the women who don't wait and go out and find their own will be married off quicker. I have heard of cases like this and it is very demotivating. Is this some sort of proven or authentic fact? What basis do people have to say this?

Hadith verification

Q: I just wanted to know the actual hadith and the reference. They were both in regards to the ummah being forgiven.

1st Hadith more or less - our Beloved Master Sallallahu Alaihi Wasallam was travelling and near the outskirts of Madina made dua 3 times and fell into sujood 3 times - was informed each time 1/3 of the ummah was forgiven each time.

2nd Hadith, the Beloved Sallallahu Alaihi Wasallam was told He would be very pleased with how Allah Ta'ala will treat the ummah on that day.