It depends on whether you are going to use continuous or categorical data and the margin of error (eg 0.03, 0.05, etc), number of regressors allowed. Eg for a population size of 500 and using a categorical data, p=0.50, t=1.96 and 0.05 margin of error; the sample size will be = 218.
You can check this reference for further clarification: JE Bartlett, IIW Joe, KCC Haggins. Organizational Research: Determining Appropriate Sample Size in Survey Research. Information Technology, Learning and Performance Journal, Vol. 19, No. 1, Spring 2001: pp 43-50.
I agree with Samer that you should first define design of your study, and this will lead to defining the sample size.
Based on your question, if you plan to use qualitative methods, the best source for informing about sample size is the the book
Lisa M. Given (Editor), The SAGE Encyclopedia of Qualitative Research Methods, Sage Publications.Thousand Oaks, 2008. (available on Internet)
where you can read several articles about sampling, e.g. SAMPLE, SAMPLE SIZE, PURPOSIVE SAMPLING, etc.
You can try to find some articles that deals with concepts such as sampling and saturation in qualitative research, e.g.
Glenn A. Bowen. Naturalistic inquiry and the saturation concept: a research note. Qualitative Research, Volume 8, No 1, pp. 137–152, February 2008. doi:10.1177/1468794107085301.
Pay attention to the quality, not just the quantity. Huge sample size does not help if measurement has been crap (i.e. non repeatable, non falsifiable, non descriptive to sufficient degree as to evaluate data gathering error).
Qualitative studies are not strong on sample size unlike quantitative studies. First you need to consider the research questions you intend to answer from the data and concentrate on how in-depth the data you collect is in answering these research questions. Additionally, depending on resources and time (it takes a lot of time to analyze qualitative data) you can decide on a number of interviews that are manageable and even once you make this decision and you set out to begin data collection, which should be reviewed at regular intervals, when you realize that you are not collecting any new information, you can stop conducting more interviews and that is acceptable
Seconding Rhoune on the approach with regards to saturation of signal in measurement.
It CAN be possible that new information is not gathered due to measurement or sampling error among other things, OTOH, it is also possible that what is to be found, has been found, which is what Rhoune is referring to, if I am not mistaken.
I can come up with many worse approaches than Rhoune's for qualitative studies...thus starting with her approach should not throw you off.
Some suggests approx. 50 qualitative interviews for a PhD, although it depends largely on both methodological and epistemological perspective. Even more important is saturation, i.e. the fact that additional data doesn't contributes materially.
See Baker and Edwards (2012) overview for a very good discussion of the topic:
Baker, S.E., & Edwards, R. (2012). How many qualitative interviews
is enough? Expert voices and early career reflections on sampling and cases in qualitative research. National Centre for Research Methods Review.
if your research is quantitative and qualitative that's mean you take biological sample then apply questionnaire ,,what is the minimum and maximum sample size
Roscoe (1975) proposes the following rules of thumb for determining sample size:
1. Sample sizes larger than 30 and less than 500 are appropriate for most research.
2. Where samples are to be broken into subsamples; (male/females, juniors/seniors, etc.), a minimum sample size of 30 for each category is necessary.
3. In multivariate research (including multiple regression analyses), the sample size should be several times (preferably 10 times or more) as large as the number of variables in the study.
4. For simple experimental research with tight experimental controls (matched pairs, etc.), successful research is possible with samples as small as 10 to 20 in size.
Reference
Sekaran, U., 2003. Research methods for business: A skill building approach. John Wiley & Sons.
Determining the sample sizes involve resource and statistical issues. Usually, researchers regard 100 participants as the minimum sample size when the population is large. However, In most studies the sample size is determined effectively by two factors: (1) the nature of data analysis proposed and (2) estimated response rate.
For example, if you plan to use a linear regression a sample size of 50+ 8K is required, where K is the number of predictors. Some researchers believes it is desirable to have at least 10 respondents for each item being tested in a factor analysis, Further, up to 300 responses is not unusual for Likert scale development according to other researchers.
Another method of calculating the required sample size is using the Power and Sample size program (www.power-analysis.com).
Your thesis should be able to stand on its own and demonstrate to your committee and the public at large your expertise in the domain and topic(s) you did research on.
In the sciences, this may include several sections of background and literature review, followed by experimental data and analysis. I’m not sure about the humanities - those requirements may be different.