I want to study probability and statistics in a deeper way than the Probability and Statistics course I had to take in the university. The problem is, my mathematical education isn't very good (on the level of Calculus 101). I'm not afraid of math, but so far all the books I could find are either about pure application, with barely any explanations, or they start with a lot of assumptions about my knowledge and introduce reams of unfamiliar notation.
I want a deeper understanding of the basic concepts. Like, mean is an indicator of the central tendency of a sample. Intuitively, it makes sense. But why this particular formula of sum/n? You can apply all kinds of mathematical stuff to the sample. And it's even worse with variance...
Any ideas how to proceed?
What do you want to learn?
Do you want to learn to do statistical analysis with a tool like R and interpret data? Do you want to learn mathematical axioms and theorems about probability and statistics and how to prove them.
Like, mean is an indicator of the central tendency of a sample. Intuitively, it makes sense. But why this particular formula of sum/n?
Depending on who you ask it's not. sum/n is the arithmetic mean. There are also other mean's like the geometric mean and the harmonic mean. Depending on the context different mean's can be used. It's ...
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