# Does descriptive statistics only work with samples?

Descriptive statistics provide simple summaries about the sample and about the observations that have been made ...

Later on, different measures are described such as 'mean', 'standard deviation' and such.. under descriptive statistics.

Does it mean "population mean" doesn't come under "descriptive statistics" category or is it only "sample mean"?

Edit:

Suppose if I want to take a mean of all 30 students in a class, then does the class represent a population or sample? I am asking this because the definitions said that "population" is something very large. But if the entire class is just 30 students then can I refer to this as population or not?

Descriptive statistics only describes the data, so you would use it only if you were interested in the properties of you data... which is rarely the case if you have a sample, unless your sample is your population, in which case this makes more sense. Descriptive statistics should more often than not be used if you have population data.

While inferential statistics would be used on a sample, to infer the properties of the population.

All is well, except that some people will argue that you never really have data for your whole population or that you have incomplete data for various reasons: changing population, measurement error,... and so these people would argue that it is better to use inferential statistics even with population data.

A population does not need to be big, the population is what you choose it to be. If you are studying students in a specific class (and you are interested in these particular students), and there are 30 students in it, then this is your whole population.

• Your statement about limiting descriptive statistic to population data overlooks all the tools of exploratory data analysis and seems to deny the utility of summarizing batches of data, no matter what their genesis. Did you really mean to be that limiting?
– whuber
Commented Oct 22, 2020 at 13:09
• @whuber No. I guess it depends on the goal as well. I think I was focusing on the goal of describing a population, regardless of the task. Commented Oct 22, 2020 at 13:16
• That's fine, but it sounds out of place as an answer to a question that explicitly asks about samples.
– whuber
Commented Oct 22, 2020 at 13:25
• In simple words, descriptive statistics can include both population and samples? Commented Oct 22, 2020 at 17:46
• @user963241 Yes, if you are interested in properties of your sample. Commented Oct 23, 2020 at 5:53

Suppose if I want to take a mean of all 30 students in a class, then does the class represent a population or sample?

It can be both, depending on your approach, your questions and your goal. Sometimes your goal may be to describe what happens in this specific class for purposes concerning this particular class. Sometimes the same class may stand in as an example from which you want to extrapolate to classes or students in general.

Whenever you are concerned with only this specific class, the class is the population. Whenever you want to generalize from your class to other classes (whether they actually exist or just be hypothetical) then this class is just a sample from the other possible classes.

Obviously you can compute the mean in both cases. However, they are not the same. The mean of the population is a fact you can compute. The mean of the sample (the second case) is an estimator that comes with a sampling error, stems from a distribution and has a standard error. Dealing with estimators instead of precise measurements, dealing with sampling error etc. is the heart of the science called Statistics.

So while computing a mean of a class that you consider a population is possible, it is mostly boring. You neither need a textbook nor a forum for that. The mean of a class that you consider to be a sample is where all those questions arise, how much you can tell about the population from your limited sample. This is where Statistics shines. This is why people use CrossValidated.

• Although much of this answer is encouraging, it downplays the value of summarizing a batch of data, regardless whether it's a sample, is considered an entire population, or is neither. The mean of a batch need not estimate anything: it describes one property of that batch and is useful to help us structure, comprehend, and reason about a collection of numbers that might otherwise be difficult to use or analyze.
– whuber
Commented Oct 23, 2020 at 13:35