Use Partem (1950) formula as:

n = ___NZ² * 0.25___

d² * (N – 1) + (Z² * 0.25)

Where n = the sample size required and which is statistically representative

N = the target population size

d = confidence level (0.05)

Z = number of standard deviation units of the sampling distribution corresponding to the desired confidence level given as 1.96.

You may also use sample size calculator by google

use Yamane's formula for sample size but that does not cover representativeness

http://edis.ifas.ufl.edu/LyraEDISServlet?command=getImageDetail&image_soid=IMAGE%20PD:PD006E3A&document_soid=PD006&document_version=98322

Where e is the error you wish to introduce (typically 0.05 or 0.01) and N is the population size

For your figures ssize will be of order of 400

For representativeness you need some profile that you know proportion of in the population to reflect into sample - usually linked to your research question eg gender, age group, areas in which they live etc.

When you have determined sample size the proportions in the sample should mirror the profile proportions you have decided upon to represent 

Regarding sampling , "representativeness" means different things to different people in different contexts. Likely here I think you mean that from a sample, you want to be able to estimate population means or totals to publish information at an aggregate level. But perhaps you want to estimate characteristics of the population distribution or have some other interest. In the first case, estimating means and totals for a finite population, I am thinking in terms of continuous data. However, you may be estimating proportions, or have an interest in discrete data.

Suppose you are looking at a finite population of size N=10,000 and suppose you are collecting continuous data and want to know what sample size, n, you need to adequately estimate a mean or total for a given item on the survey. If you did a simple random sample, then various sample survey books, such as Cochran, W.G.(1977), Sampling Techniques, 3rd ed., John Wiley & Sons, pages 77 and 78, could give you the information needed. You will see that a preliminary estimate of the variance of the data is needed. Cochran suggests you obtain this by means of a pilot study, or previous similar data or another educated 'guess.' This is true also for model-based sampling, which I assume you will not be using. (However, if you have regressor data, they could be put to good use.)

This is a common problem for sample size estimation: you need some preliminary information on the variance of each item (variable of interest or 'question') first. An exception of sorts is estimation of proportions, which can assume a worst case (p=q=0.5) when estimating sample size needs.

But the fun does not stop there. It is rare that a population as large as yours should use a simple random sample, even if strictly probability sampling and estimation (no 'auxiliary'/regressor data available) is used. You are likely to do much better by grouping your population into strata. (That works well for regression models as well.). The idea of stratification is to obtain more accurate results (re sampling error) with a smaller overall sample size (which can also help with nonsampling error, particularly measurement error). But if you want to publish information such as totals separately by those strata, that is not really stratification. It will not lower your sample size, but raise it because you are trying to publish more categories.

Stratification lowers your sample size need by grouping parts of the population that are more alike in that there is less variance between members of a given stratum. Optimum allocation and other sample size information can be found in books like Cochran's (chapters 4 and 5 there, for simple random sampling and for stratified random sampling).

There are other design considerations, such as cluster sampling and complex survey sampling that may be beyond the scope of this question.

Whatever the type of data you are collecting, and whatever design and/or regressor data you have, a sample size is generally picked with the idea that you have some accuracy level that you want to obtain, and you want to know how many observations it will take to do that. Besides the sampling error concerns that predominate in whatever sample size estimator you choose, remember that if you try to collect too much data, that can lower your data quality and invalidate, to a degree, the variation you estimated to estimate sample size to begin with.

Note that there are methods to sample, and methods to estimate, and some go together and others do not.

There are a number of good books available.

Cheers

Use Partem (1950) formula as:

n = ___NZ² * 0.25___

d² * (N – 1) + (Z² * 0.25)

Where n = the sample size required and which is statistically representative

N = the target population size

d = confidence level (0.05)

Z = number of standard deviation units of the sampling distribution corresponding to the desired confidence level given as 1.96.

You may also use sample size calculator by google

Hi Joynal

In order to determine your sample size, you need to establish the level of confidence that you would want to attach to your sample eg. you can use 95% mostly  used  in quantitative research; 90% cheaper depending on available resources and time; 99% most accurate one assuming all the resources are available.

You can the use the formula for determining sample sizes.  n = N/1+(N*(e)2 (Where N = 10,000, and e = .05 at 95% confidence level

in that case your sample size n = 10,000/1+(10,000*(0.05)2

n = 10,000/1+10000(.0.0025)

n = 10,000/1+ 25

n = 10000/26

n = 384.6

n = 385 Representative sample