For my project, the first step of designing a service is design research. how many people should I interview to reach the point of synthesizing the interview results? is there any to go place to find out about these steps?
Academic studies tend to say between 8-12 is optimal for qualitative research. However if you are targeting discrete groups of users (e.g. teachers and students) you may need 8-12 of each discrete type. In my experience, the cost starts exceeding the benefit after about the 8th participant.
The following factors should also be taken into account:
- interview structure and content
- complexity of research
- level of certainty required for research outcomes
- cost of resources
- heterogeneity of sample
Sources: Mason (2010), Guest et al. (2006), Ryan and Bernard (2006)
A useful academic article can be found at http://www.qualitative-research.net/index.php/fqs/article/view/1428/3027
While referring specifically to usability, the following article by Nielsen states that five are already enough to find out a lot of issues. This is close to the 8-12 rule mentioned by danimu:
I also remember reading about a "rule of thumb" for qualitative research that goes like this: "Issue mentioned by one participant is an anecdote. Mentioned by two is a coinsidence. Mentioned by three is a trend worth to investigate." (sorry for lack of cite source)
So at least three participants would be required but due to high possibility of one missing something she wanted to mention, a size of 3x3 (==9) participants would be a more reliable size to go.
I personally try to avoid going in with a fixed number in mind.
Instead I treat it as a continual process where we carry on interviewing while we're still learning new things (sometimes called the saturation approach). The point where we're start hearing the same stories repeatedly is the point where we move the focus from research to analysis and synthesis.
Sometimes that'll be after the fifth of sixth person we talk too. Sometimes we'll still be learning new things on person thirty.
The paper referenced in @danimu's answer talks about saturation) quite a bit and is well worth a read.