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.
- 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.
- Slightly more academic but nonetheless good starting point will be introduction to probability and statistics by Sheldon Ross.