Central tendency describes the typical value of a variable.Measures of central tendency by level of measurement are covered including the mean, median, and mode.Appropriate use of each measure by level of measurement is the central theme of the chapter.The chapter shows how to find these measures of central tendency by hand and in the R Commander with detailed instructions and steps.Skewed distributions and outliers of data are also covered, as is the relationship between the mean and median in these cases.

Chapter 3 covers MEASURES OF LOCATION, SPREAD, AND SKEWNESS and includes the following specific topics, among others:Mode, Median, Mean, Weighted Mean,Range, Interquartile Range, Variance, Standard Deviation, and Skewness.

Chapter 3 covers measures of location, spread and skewness and includes the following specific topics, among others: mode, median, mean, weighted mean, range, interquartile range, variance, standard deviation, and skewness.

A review of basic probability theory – probability density, expectation, mean, variance/covariance, median, median absolute deviation, quantiles, skewness/kurtosis and correlation – is first given. Exploratory data analysis methods (histograms, quantile-quantile plots and boxplots) are then introduced. Finally, topics including Mahalanobis distance, Bayes theorem, classification, clustering and information theory are covered.

This chapter discusses two types of descriptive statistics: models of central tendency and models of variability. Models of central tendency describe the location of the middle of the distribution, and models of variability describe the degree that scores are spread out from one another. There are four models of central tendency in this chapter. Listed in ascending order of the complexity of their calculations, these are the mode, median, mean, and trimmed mean. There are also four principal models of variability discussed in this chapter: the range, interquartile range, standard deviation, and variance. For the latter two statistics, students are shown three possible formulas (sample standard deviation and variance, population standard deviation and variance, and population standard deviation and variance estimated from sample data), along with an explanation of when it is appropriate to use each formula. No statistical model of central tendency or variability tells you everything you may need to know about your data. Only by using multiple models in conjunction with each other can you have a thorough understanding of your data.

We introduce the most commonly encountered data types and their properties. We describe the process of data sampling, focusing on the distinction between the sampled statistical population and the collected sample, stressing the need for a carefully designed sampling strategy. We introduce the sample statistics that form the core of data analysis, characterising both the position of values (arithmetic mean, median and others) and the spread of values (e.g. variance). The visualisation of individual variables by histograms and box-and-whiskers plots is introduced and later demonstrated with R code. We also briefly discuss the concept and properties of distribution and probability density functions, addressing discrete and continuous variables separately.

We introduce variates (random variables), defining their cumulative distribution function (c.d.f.) and probability density function (p.d.f.). We give the two main decomposition theorems of c.d.f.s, Jordan and Lebesgue, and the unifying Stieltjes integral approach for continuous and discrete variates. We study properties and descriptions such as symmetry, median, quantiles, and the quantile function, and modes of a distribution. The mixing of variates is also studied, including the famous example of Student's t, which can be represented as a mixed-normal variate.