Descriptive Statistics and Discrete Probability Distributions

Abstract

In this chapter, we introduce several fundamental aspects of statistics: its language, quantities used to describe data, visualization of data, discrete probability distributions, and terms that describe measurements. For the language of statistics, we define such terms as experiments, random samples, bias, and probability. For the quantities that describe data, we define the mean, median, mode, quartiles, expected value, unbiased variance, and covariance. For visualizing data, we discuss histograms, box-whisker plots, and scatter plots. Discrete probability distributions, the cumulative frequency function, the probability mass function, and the binomial distribution and the Poisson distribution are defined. Then, the concept of independent random variables and its significance is discussed. Lastly, terms used to describe measurements are defined and illustrated: accuracy, precision, repeatability, reproducibility, and stability.