Respected sir, You are right, and that's why we add a sapling error and the degree of freedom while analysing. And on the basis od that only we decide the recommendations. In such a case, the findings are not 100 per cent accurate but we can roam around the actual one.

I am not an expert of statistics, but in my researchers, I have a very less belive on my sample survey analysis and its report. In my all researches of the social sciences with before sample selection and after the analysis before interpretation and recommendation, I always conduct Participatory Learning Approaches to understand and triangulate the findings. It also helps to rectify the mistakes and tested with the local experience of many years through community triangulation.

If I am wrong Please correct me.

Thank you

Collins -

"Representativeness" is not straightforward. If you knew your sample to be a smaller version of your population, then that would imply you already knew all there was to know about the population, so what do you expect to learn from a sample?

Note that in Ken Brewer's article he wrote for his Waksberg Award, Brewer(2014), "Three controversies in the history of survey sampling," Survey Methodology, Dec 2013,

https://www150.statcan.gc.ca/n1/pub/12-001-x/2013002/article/11883-eng.htm, that in Section 2, "The First Controversy: Anders Kiaer and the 'Representative Method'" he notes how the effort to make a purposive sample match characteristics of a population can fail. Still it can be worth an effort. See this paper by Richard Valliant, https://www.researchgate.net/publication/331481770_Comparing_Alternatives_for_Estimation_from_Nonprobability_Samples, and note my first comment there on that paper. Also note that in one of my projects, https://www.researchgate.net/project/Cutoff-and-quasi-cutoff-sampling-with-prediction-for-Official-Statistics, there is an update, "Representativeness - various meanings of a 'representative sample'."

Ken Brewer's article shows that we can have inference from using the probability-of-selection (randomized/design-based) approach, or the model-based approach, or one can use a combined approach. From Richard Valliant's paper above, and also from work by Mike Brick and others, we can get some information from nonprobability samples. Note in the Valliant paper that the model-based approach does well in simulations, but a combined approach also using a reverse engineered pseudo-random approach might do better.

Most people have heard of random sampling. There are various designs. If you are unfamiliar with the model-based approach, here is a good, basic explanation: "The model based (prediction) approach to finite population sampling theory," Institute of Mathematical Statistics Lecture Notes - Monograph Series, Volume 17, 1992, 225-240, Richard M. Royall, 

 https://www.researchgate.net/publication/254206607_The_model_based_prediction_approach_to_finite_population_sampling_theory/. 

Project Euclid has provider this paper, open access: 

 https://projecteuclid.org/euclid.lnms/1215458849. 

So to infer to the population from a sample, representativeness may be a good concept, but the bottom line is often measuring a total or subtotal, and you may do that as long as your methodology can provide good results from your sample. Thus your concept of representativeness might be expanded to mean successfully learning what you need to learn about a population, from a sample, using appropriate estimation/prediction methodology.

The idea of random probability sampling could be said to be to likely find a "representative" sample, and estimate variance and perhaps bias based on the idea that over a large number of trials, "on average," you do have good results. However, we only get one sample, and by bad 'luck,' one could have a sample that a glance could tell you would not fit many people's idea of being representative. A model-based approach, however, means that you rely on auxiliary/regressor/predictor/covariate data to guide your sample to (model) 'represent' your population. Such covariates take us back to the idea of constructing a representative sample based on knowledge of the characteristics of the population, but instead, we use covariates to model/modify the sample data to infer up to the population.

The current question emphasizes environmental science. I would assume we are still in need of covariates. Data are needed on related information so that your sample can properly infer to your population. At the lowest level, one could use characteristics of the population to at least stratify, or divide the population into subpopulations, so that you can sample each separately. At much higher levels of covariate information, one might use regression modeling to great advantage. Randomization is often helpful.

Best wishes - Jim

@knaub. Thank you for painstakingly responding to Jim. I have my contributions in the area of sciences and environmental sciences. Some scientists take few samples for analysis because of the huge cost involved in the analysis of the samples. Though results would be used for drawing inferences, could we say that those samples were representative? This is obtained in chemistry, biological sciences, etc. High cost of Analysis may influence the representatives of samples. On the other hand, using a non probability sampling method poses a problem to how representative a sample would be because here it may be difficult to determine the sampling error and various measures of precision. From these, our interpretations and conclusions, to a degree, may not be accurate; though useful.