The definition disagrees with you. Facts are just that - facts. The analysis of how you arrived at that fact is statistics. It requires numerical analysis. If you've ever taken a stats class you'd know an answer like "more than average" without any numerical work shown would be marked wrong. You'd also know that saying "more than average" provides no real information since it's a huge range.
Average of X > average of Y fits “a collection of quantitative data”
For more detail, I have taken statistics, even tutored PHD students.
Showing your work is required if the answer is 4.415 or more than average. A sample refers to a single element, statistic encompass a sample, a parameter covers to the full population.
You will often hear statistics communicated as something like “more than four times as likely” and assume it’s referring to 4<X<5 but they can also be used in cases when a measurement exceeded the range at which you can quantify it. As in you checked the rain gauge and it was full, in such cases the only option is to use > X.
I don't think that meets the definition. Where is the collection - there isn’t one. Without showing your work, why should I believe a "fact" you present? You need to prove a fact. That's where statistics is helpful. Maybe you did tutor people from a pure math perspective. You might need to learn how to actually apply statistics in real life.
None of the stuff you mention actually means anything when you try to apply it to policy if you don't know how the result was achieved, what it's actually measuring, and what the baseline is. Any good statistical analysis will cover this as well as things like biases, corrections, and confidence. Otherwise I could give you a fact of my opinion is more liked than your opinion...
The samples that make such a calculation true. That’s what you’re missing an actual statistic X>Y is based on the underlying data.
Further someone can just as easily make up X = 27.24 +/- 0.01 with a 95% confidence interval as X > Y, it’s the actual data that makes something a fact rather than an option.
“None of the stuff you mention actually means anything when you try to apply it to policy if you don't know how the result was achieved, what it's actually measuring, and what the baseline is.” Again that applies equally to all statistics and you can provide them just as easily with either format.
