i didn't understood what you mean with "can descriptive"... sure that you can to use a descriptive statistical for to know about sex, age, social economic status or something... what's your doubt?

Yes, descriptive statistics techniques can be used on data from a large N=200 purposeful sample. Descriptive statistics are used to summarize and describe the main features of a dataset, such as the central tendency, variability, and distribution of the data. They can be used to identify patterns and trends in the data, and to make comparisons between different groups.

When using descriptive statistics on data from a large sample, it is important to keep in mind the following:

• The sample should be representative of the population of interest.
• The sample size should be large enough to provide accurate results.
• The appropriate descriptive statistics techniques should be used for the type of data that you are analyzing.

Here are some examples of descriptive statistics techniques that can be used on data from a large N=200 purposeful sample:

• Central tendency: Measures of central tendency, such as the mean, median, and mode, can be used to describe the typical value in the dataset.
• Variability: Measures of variability, such as the standard deviation and range, can be used to describe how spread out the data is.
• Distribution: Histograms, boxplots, and other graphical techniques can be used to visualize the distribution of the data.

Descriptive statistics techniques can be used to answer a variety of questions about data from a large N=200 purposeful sample. For example, you could use descriptive statistics to answer the following questions:

• What is the average age of the participants in the study?
• What is the range of incomes of the participants in the study?
• What is the distribution of political party affiliation among the participants in the study?

Descriptive statistics techniques are a valuable tool for understanding data from large samples. They can be used to identify patterns and trends in the data, and to make comparisons between different groups.

Here are some additional tips for using descriptive statistics on data from a large N=200 purposeful sample:

• Use appropriate statistical software. There are many different statistical software packages available, such as R, SPSS, and Stata. These software packages can help you to calculate descriptive statistics and to create graphical visualizations of your data.
• Consult with a statistician. If you are unsure about how to use descriptive statistics on your data, you should consult with a statistician. A statistician can help you to choose the appropriate statistical techniques and to interpret your results.

Descriptive statistics can also be used to confirm the validity of your data set, even with higher populations than 400. As described by Ahlam Hanash Gatea you can get central tendency, variation, etcetera, but you can also use it to check that the values are as "expected". Do you have outliers? Are the outliers normal or abnormal values (i.e. do I keep or remove). If I have missing values, should I remove the entire observation, replace with a value (mean, regression...), or just leave as it is?

I see many students or researchers who have no idea of the validity of their information. They think statistics can fix anything. But most of data come from processes involving automated measures and human activities, there must be errors in the resulting dataset. Should be checked.

Boxplot should be one of our friend in this descriptive/understanding work.

The issue here is not your sample size, it is that your sample is non-random (i.e., purposive). You thus have not way to generalize to the actual population values (e.g., the mean in the population).

As David notes, your sample appears to just represent itself. If it were the entire population (as indicted by a capital "N") then the descriptive statistics would be meaningful.

If this is a sample from a larger population and you want to infer to that population, then there are two main ways to do this: 1) the probability of selection approach (design-based), and 2) the model-based approach. Only the latter case could be used for a purposive sample. For the model-based approach you need predictor data on the entire population.

Work has been done to infer to the population from nonprobability samples, but in many cases this may have low accuracy and require a number of covariates for which you probably won't have data. At least one covariate on the entire population is needed. Often many covariates are needed, and the more that are needed, the less accurate I expect you will be, with bias as the elusive problem. See the following:

Elliott, M.R., and Valliant, R.(2017), "Inference for Nonprobability Samples," Statistical Science, 32(2):249-264,

https://www.researchgate.net/publication/316867475_Inference_for_Nonprobability_Samples, where the paper is found at

https://projecteuclid.org/journals/statistical-science/volume-32/issue-2/Inference-for-Nonprobability-Samples/10.1214/16-STS598.full (Project Euclid, Open Access). 

The most accurate purposive sampling is likely quasi-cutoff sampling with ratio modeling for repeated surveys for Official Statistics. That has proven highly accurate. See the following:

"Application of Efficient Sampling with Prediction for Skewed Data," JSM 2022: 

https://www.researchgate.net/publication/362370770_Application_of_Efficient_Sampling_with_Prediction_for_Skewed_Data ,

which includes comments on

Guadarrama, Molina, and Tillé(2020), in Survey Methodology, which found that regression modeling appeared to perform better than calibration in small domains, for cutoff sampling, in their excellent article found at https://www.researchgate.net/publication/342657185_Small_area_estimation_methods_under_cut-off_sampling. 

Also note the following:

https://www.researchgate.net/publication/374294842_Stratification_and_other_Issues_for_Best_US_Federal_Establishment_Survey_Quasi-Cutoff_Sampling

I noted above that "Only the [model-based approach] could be used [with] a purposive sample" for inference to a population. (That requires predictor/covariate data.) However, note that in the article I referenced above by Elliott and Valliant (and other work by Valliant and others) they use "pseudo-inclusion probabilities" which, as in the case of models, rely on covariate data. So there is that approach as well.