Are there any good popular science book about statistics or machine learning? There a bunch of really good popular science books around, that deal with real science, as well as the history and reasons behind current theories, while remaining extremely enjoyable to read. For example, "Chaos" by James Gleick (chaos, fractals, nonlinearity), "A brief history of time" by Stephen Hawking (physics, origin of the universe, time, black holes), or "The Selfish Gene" by Richard Dawkins (evolution and natural selection). Some of these books present arguments (Dawkins) and some don't (Gleick). But they all serve to make it easy for those of us without in-depth scientific education to understand otherwise difficult concepts.
Are there any such books that focus mainly on Statistics, or machine learning?
Please include a summary of what each book covers.
 A: "The Theory That Would Not Die" by Sharon Bertsch McGrayne is a very readable book on the history of Bayesian statistics and the general idea behind it without getting too bogged down in the math.
I am also a fan of "The Cartoon Guide to Statistics" by Gonnick and Smith as a nice introduction to the general concept of statistics with some of the math, but presented in a way that does not put you to sleep (I also have the cartoon guides to genetics, physics, and chemistry and have read a couple of the others).
A: I would suggest the following books, though neither is ideal, you should check out:

*

*The (Mis)Behaviour of Markets by (the great) B. Mandelbrot

*Struck By Lightning by Jefferey Rosenthal

with the former more focused on finance, but still statsy, and the latter is a introduction to all the interesting probability subjects: odds, the Monty Hall problem, utility functions, random walks etc.
A: A very good book for aiding basic statistical literacy and  statistical reasoning  - and for making the case for these as important - is The Tiger That Isn't by Andrew Dilnot, the former presenter of a popular radio show about applied statistics for the BBC.
I often recommend it as the statistics equivalent of the popular pop science book Bad Science by Ben Goldacre. It's good for introducing basic statistical reasoning, for showing the importance of basic statistical reasoning, and getting people concerned about the lack of basic statistical reasoning among people who really should know better (particularly politicians, journalists, etc). Very accessible, engaging, funny in places, deeply worrying in others! Particularly good as an introduction for anyone who thinks of numbers as 'not their thing'.
A: Ian Ayres is author of the book "Super Crunchers: Why Thinking-by-Numbers Is the New Way to Be Smart" which discusses several examples of data mining. 
A: The Drunkard's Walk by Leonard Mlodinow is an easy to read introduction to basic stats and probability. The content is aimed at an audience with no statistical or mathematical training, and there are no equations. I found it a little too dumbed down. There are lots of anecdotes relating various applications of bad statistics, and clear explanations of why they were wrong. 
The book covers basic stats and conditional probability.
A: I figured I'd fill in a gap here by pointing out a few good mass market-style books on fuzzy sets, information theory, entropy and statistical reasoning that I've read and highly recommend. 
• For all things fuzzy, a good informal starting point is McNeill, Dan, 1993, Fuzzy Logic. Simon & Schuster: New York.
• For a good mass market intro to neural nets, organized around some interesting speculations about the organization of the human brain, see Hawkins, Jeff, 2004, On Intelligence. Times Books: New York.
For easily readable introductions to important topics like the pitfalls of statistics and fallacious reasoning, try these three:
• Huff, Darrell, 1954, How to Lie with Statistics. W.W. Norton & Company    New York.   
• Kault, David, 2003, Statistics with Common Sense. Greenwood Press: Westport, Connecticut. 
• Smith, Gary, 2014, Standard Deviations: Flawed Assumptions, Tortured Data and Other Ways to Lie with Statistics. Overlook Press: New York.    
The following are all related to information theory and entropy:
• Lucky, R. W., 1989, Silicon Dreams: Information, Man, and Machine. St. Martin's Press: New York.
• This author does an excellent job of putting information theory in context and pointing out abuses of it, while still writing in a way a non-specialist can grasp: Pierce, John Robinson, 1961, Symbols, Signals, and Noise: The Nature and Process of Communication. Harper: New York.
• I read this similar title, but can't remember if it's a later edition or a follow-up: Pierce, John Robinson, 1980, An Introduction to Information Theory: Symbols, Signals & Noise. Dover Publications: New York.
• If I remember right, this author was easily readable, while still getting into some more advanced concepts: Brillouin, Léon, 1964, Science, Uncertainty and Information. Academic Press: New York.    
• Also see Brillouin, Léon, 1962, Science and Information Theory. Academic Press: New York.
• I read this long ago, but believe this author was readable and had some interesting observations on information theory: Bar-Hillel, Yehoshua, 1964, Language and Information: Selected Essays On Their Theory and Application. Addison-Wesley Pub. Co. Reading, Mass.
I want to caution that the mass market books on mind-blowing topics like chaos, information, quantum physics, probability, randomness, "Cybernetics," self-organization, fuzzy sets and artificial intelligence contain a small but prominent minority of material that is blown way out of proportion, sometimes to the point of being logically invalid. Each of these theories has well-known proponents who don't know when to stop with a good thing and make huge logical leaps to turn their particular fields into grandiose explanations of everything. Each has authors that go way beyond the evidence, even to the point of ignoring explicit warnings by the founders of their fields, as Shannon did about misuses of information entropy. There is a feverish, unhealthy tint to their writing, which in sometimes qualifies as junk science produced by cranks. I could name some famous names who continue to print outrageous things about these topics, based on obvious logical fallacies and sometimes grossly mistaken points of fact. I won't do that here to avoid a serious flame war, because I'd have to call out some idols and sacred cows. Just be aware that misleading material of this kind is out there and be ready to red-flag it. Watch out for extraordinary claims without the requisite extraordinary proof.
A: I suspect The Lady Tasting Tea, by David Salsberg is exactly what you want.  It's very much written in a narrative style, almost like a novel, with essentially no math (as I recall), so it would be accessible to anyone.  I read it long ago and really enjoyed it.  It reads very fast, and could give people a sense of what statistical analysis is about and how it can help us understand the world and solve practical problems.  
A: The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World is a book by Pedro Domingos released in 2015. Domingos wrote the book in order to generate interest from people outside the field.

The book outlines five tribes of machine learning: inductive
  reasoning, connectionism, evolutionary computation, Bayes' theorem and
  analogical modelling. The author explains these tribes to the reader
  by referring to more understandable processes of logic, connections
  made in the brain, natural selection, probability and similarity
  judgements. Throughout the book, it is suggested that each different
  tribe has the potential to contribute to a unifying "master
  algorithm".

https://en.m.wikipedia.org/wiki/The_Master_Algorithm
A: Nate Silver's new book The Signal and the Noise: Why Most Predictions Fail – But Some Don't fits your description quite well. It is also an introduction into Bayesian thinking for laypeople. It got some attention lately and a review of the book can be found here.
Also worth checking out are Levitt & Dubner's Freakonomics books. 
A: More good reads:
The Flaw of Averages by Sam L. Savage
Fooled By Randomness by Nassim Taleb
Both are somewhat cautionary books about being careful towards how to interpret probability and statistics in our everyday lives. For example, in financial markets, one might misuse an everyday gaussian distribution as a risk measure with disastrous consequences, and thus we might want to use more empirical based models (such as monte carlo simulations) in practice. Taleb is very popular in financial circles, and often cautions us to be more careful about behavioral biases and over-reliance on modelling 
A: Numbers Rule your World, by Kaiser Fung, describes the importance of statistics in a lot of systems that are fundamental to modern society, like insurance markets.
Number Sense, also by Kaiser Fung, talks about "big data" more specifically.
