Statistics is not about numbers. It is about what numbers mean — and more importantly, what they don't.
Before you calculate a mean, run a regression, or test a hypothesis, you have already made a decision that determines whether your answer is meaningful or nonsense: you decided what kind of thing you were measuring. A student's nationality and a student's exam score are both numbers in a spreadsheet. One of them you can average. The other one you cannot. The difference between the two is the entire foundation of statistical analysis.
The true parameter (like the average height of all humans) is fixed but unknown. The statistic (the average height of your sample) is known but constantly moving. Every time you draw a new sample, the statistic changes.
Notice how the sample means build their own distribution around the true population parameter.
The branch of statistics you are using depends entirely on the claim you are trying to make. Are you describing what you already have, or are you trying to infer what you don't know?
Mean ()
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Descriptive statements report facts about the sample. Inferential statements make leaps of faith about the population.
Not all numbers are created equal. The level of measurement dictates what mathematical operations are legally allowed to be performed on the data.
Notice how higher levels of measurement inherit all the permissions of the levels below them.
Quantitative data must be further split based on how it is gathered. If it's counted, it's discrete. If it's measured, it's continuous. Use the scanner to see how different lenses extract different data from the same object, then test your intuition.
Variables
A characteristic of a population or sample.
Exercise: Scenario Classification
"He is 19 years old. His mother is a teacher. He has 3 brothers. He got a 'B' in the course."
Every piece of information in that statement represents a specific type of variable. Drag and drop the extracted concepts into their correct classifications.
Be careful with money and time — they can be tricky to classify depending on the context.
"How to actually do statistics, step by step."