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I have some solid unterstanding of math basics and want to learn more about statistics. I'm following a stats course on Khan Academy that has roughly this content:

  • Summarizing quantitative data
  • Modeling data distributions
  • Exploring bivariate numerical data
  • Study design
  • Probability
  • Random variables
  • Sampling distributions
  • One-sample confidence intervals

Now, I'm a few hours in the course and feel the need for an additional reference besides the course.

For example, in the course, in some video, the interquartile range/spread is introduced very briefly. It is shown with an example how to calculate the IQR, and in the end we arrive at some number but it's not really well explained why this makes sense to calculate the IQR we do or what it actually represents.

So I'm looking for a book that teaches the basics in a clear way and also explains why a number (for example IQR or variance) makes sense and what we can infer from it. If the book also has some basic mathematical reasoning behind the formulas presented, I would also like that.

I heard on this site about the book "Statistics" by Freedman/Pisani/Purves. I wasn't able to look at the contents of that book and was wondering if it would be the right book in my case.

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Statistical Reasoning by Gary Smith: tons of practical examples and very very readable explanations. Old gem.

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Pisani et al. is a great book. I highly recommend it.

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    $\begingroup$ Presumably, Freedman, Pisani and Purves, Statistics (New York: W.W. Norton). Thoroughly agree. $\endgroup$ – Nick Cox Jan 2 '18 at 12:19
  • $\begingroup$ Yes. I think the authors are in different order on different editions, but I could be misremembering. $\endgroup$ – Peter Flom Jan 2 '18 at 20:59
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    $\begingroup$ The order of authors remained Freedman, Pisani, Purves in all four editions. Ani Adhikari was given as fourth author for the second edition. David Freedman is no longer with us. $\endgroup$ – Nick Cox Jan 3 '18 at 13:55

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