Abstract
Statistics can be defined as the collection, classification, analysis, and interpretation of data. It is a mathematical discipline traditionally divided into two fields: descriptive statistics and inferential statistics. It makes use of the tools and methods of probability theory. Nowadays, statistics is an interdisciplinary knowledge area, used in any field where data analysis is needed. This chapter deals with descriptive statistics and probability, including central tendency measurements, variability measurements, random variables, and probability distributions, with a special focus on the binomial and normal probability distributions.
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- 1.
In what follows we will use both “variable” and “characteristic.”
- 2.
For the simplest example of tossing a coin, the total outcomes possible are 2, and the number of favorable cases for the event Heads is 1. Thus the probability of getting heads is \(\frac{1} {2} = 0.5\).
- 3.
The cdf is also suitable for discrete distributions.
- 4.
As a result of the fact that \(V ar[<CitationRef CitationID="CR4">69</CitationRef>] = E[{(X - \mu )}^{2}]\).
- 5.
We assume that these are the values defined in our manufacturing process.
References
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Hsu, H. (2010). Schaum’s outline of probability, random variables, and random processes. Schaum’s Outline Series (2nd ed.). New York: McGraw-Hill.
Jakir, B. (2011). Introduction to statistical thinking (with r, without calculus). http://pluto.huji.ac.il/~msby/StatThink/index.html. Accessed 01.08.2011.
Montgomery, D. (2005). Introduction to statistical quality control (6th ed.). New York: Wiley.
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Cano, E.L., Moguerza, J.M., Redchuk, A. (2012). Statistics and Probability with R. In: Six Sigma with R. Use R!, vol 36. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3652-2_9
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DOI: https://doi.org/10.1007/978-1-4614-3652-2_9
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