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This question already has an answer here:

I am looking for an elementary statistics book, that contains topics such as descriptive statistics, sampling distributions of the mean and variance, etc. However, despite my interest in basic topics, I am looking for a book that teaches it in a high level, for example: when discussing the why the variance includes a squared difference from the mean and not absolute value, I am looking for a mathematical explanation (the problem with the derivative), or, a loss function explanation. In other words, I am looking for an elementary statistics book for mathematicians or statisticians, and not just a textbook. Can you please recommend me of such books, if exist? Thank you.

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marked as duplicate by kjetil b halvorsen, Silverfish, gung, John, mpiktas Sep 1 '16 at 16:19

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ Have you checked: stats.stackexchange.com/questions/tagged/references ? $\endgroup$ – Tim Aug 31 '16 at 13:32
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    $\begingroup$ I have already posted a recommendation for Kiefer's monograph at stats.stackexchange.com/a/66059/919 and so will not repeat it here. The mathematical level is not high--it assumes only elementary calculus and a little linear algebra--but the conceptual level is extremely high. Reading it might help you refocus your interests a little, too: away from technical mathematical issues like differentiability and towards fundamental statistical issues such as comparing risk functions. $\endgroup$ – whuber Aug 31 '16 at 13:45
  • $\begingroup$ Have a look at this (and the links it contains): math.stackexchange.com/questions/735075/… $\endgroup$ – kjetil b halvorsen Aug 31 '16 at 16:22
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    $\begingroup$ You may have different needs to the thread proposed as a duplicate, but on their face the two threads look very similar (both seeking elementary statistics texts for someone coming from a mathematically strong background). It might be worth editing your question to make clear why your needs are different, if you do not feel that that thread is relevant to your case too. $\endgroup$ – Silverfish Aug 31 '16 at 17:12
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  1. The best one (subjective, in my opinion) will be introduction to statistical reasoning by Gary Smith. This book is worth its weight in gold for elementary statistics and is filled with tons of real world examples and stories.
  2. Slightly more academic but nonetheless good starting point will be introduction to probability and statistics by Sheldon Ross.
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