Is it so that some forms teories before they know all the data?
In math, mathematicians do not seek for any external empirical data to arrive at new theory, CMIIW.
And some does not form it until they got a lot of data?
In a lot of scientific disciplines, as the teacher say, scientist are supposed to only draw conclusion after data gathering. But the problem with this is that empirical data could never be completely collected for many reasons. One of the reason why is that our senses capabilities that we use for data gathering is by itself is limited. A good example when conclusion was false. There used to exist a belief that the earth was flat, which turned out to be false: earth is never flat. It is always round. It was their conclusion that was a mistake.
When we use our eyes for data gathering for example, the range of observations is limited. If you want to observe farther, you'll need telescope, binoculars. When you need to observe substance that is very small in measurement, you'll need microscope. Some may not be able to observe using their senses nature capability in data gathering so that they could reach a scientific conclusion, since the supporting observation tool may not have been available or invented for them.
Some scientist have found that human ear, has a range of audible frequency of sound: 20-20000hz. Less than 20Hz, is an infrasonic, more than 20000Hz is ultrasonic, which is just out of range of our hearing sense.
Imagine that we put too much rely on using five senses in perceiving things, what would our conclusion be like?
When you hear nothing,you could just draw a conclusion there was no sound, while there could be an infrasonic sound that is out of range of our hearing sense.
And anyone could reach the same conclusion as medieval society that believed that earth was flat before they are shown the photograph. The medieval society may not have had the chance to observe from outer space and taken picture of the earth so that it was clear for them the earth was not flat.
Not to mention that the ability to reach a place where data can be founded. When an empirical evidence is not at the same place as the observer, they need to go to the place. But going to a place, means the observer need to spend money at least for transportation and accommodations. An archaeologist, who visit some "excavation site "to find whether they can gather an artifact, etc, and induce something from it. They may not have the financial support to perform this.
In a market research company, some even have to pay a lot of interviewers just to search for them many respondents for their research to fill some questionnaire. This is an endeavor that simply can't feasibly be executed by an individual.
I am inclined to say that many at least psychologically will reach to a conclusion anyway, although they have no sufficient supporting data. Remember, it is just a scientific teaching anyway; and some may not hold the scientific virtue.
Even if scientist do their best to try to conform to the virtue, The lessons I learnt is Scientific knowledge subject to constantly changing when there founded a new evidence from observation, experiement, that human weren't able perform in the past, because there were no invention of observational device that enables themselves to perform their observation yet.
But I found mathematical knowledge don't share the the same characteristics as scientific ones. You may find that many of them have been discovered for thousand of years yet still unchanged.