Question about a question "How does changing the mean and standard deviation affect descriptive and inferential statistics?

Statistics Intro

One of the most frequently asked questions How does changing the mean and standard deviation affect descriptive and inferential statistics?

had a very interesting answer that made me think

"I think this illustration may be causing some confusion - it is meant to show you what different types of datasets might look like. In actual analysis, one would not “set” the mean or standard deviation, one would find them, based on the dataset.

In descriptive statistics, one would observe the data and calculate the mean and standard deviation, which you could then report. As for inferential statistics, a larger standard deviation means a wider curve - the individual data points are more evenly distributed. The mean is simply the average. What can be inferred depends on what the data describes. Inferential statistics need some background knowledge to draw conclusions from the data.

TL;DR: You wouldn’t normally change the mean and standard deviation yourself. You would find/observe/report them based on the data. The exercise was for demonstration purposes."

this means the question itself might not make sense. because you would not really change the standard deviation or mean, you would always have to calculate them.

still assuming you calculated them wrong, wouldn’t that effect the inferential statistics. since you draw a conclusion basically from what you calculated?

I say this because according to this really great youtuber Descriptive Statistics vs Inferential Statistics

thank you all for taking the time to read


As noted, the phrasing of the question maybe misleads as to the purpose of it, but it does have some potential context. I’ve seen it employed as a rhetorical device (e.g.: what happens to the area of a rectangle if we change the lengths of the sides).

There are 2 separate notions:

  • that there could be a transformation going on.
  • the existence of 2 distinct items which are being compared.

However, unless explicitly stated, it’s more often the 2nd of the two options that happens to be the case (unless the topic is transformations).

As a final note, as much as maths aim to be precise, notation and language can sometimes get in the way of their clarity. I have seen, more than once, an author apologize for an abuse of notation and then go ahead and use that same notation (for the sake of not getting mired in formality). Or, in another case, an author will say (paraphrasing here): “clearly, this notation is ambiguous, but the reader can deduce which meaning is meant from context”.



thanks for your answer.
The problem for me as a non-native English speaker is that sometimes I take things explained in a very literal sense

that is why I personally felt very lost, but it might be one of those things that you just lose yourself thinking about, then you would go on with your day clean the dishes or something and then it clicks in your head and you understand it.


I completely understand. English is also not my first language! And technical books present a whole new set of challenges in that sense.

Which is why it’s nice to have forums to ask around :slight_smile: