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.

This chapter introduces the framework for exploring emoji-text relations in social media that is used in this book. The chapter begins by explaining the discourse semantic systems that have been developed in Systemic Functional Linguistics for describing ideational, interpersonal, and textual meaning. This is in order to lay the foundation for exploring the linguistic meanings with which emoji coordinate in subsequent chapters. The chapter then introduces the concept of ‘intermodal convergence’ used in social semiotics to describe how semiotic modes such as language and images coordinate to make meaning. The chapter outlines the principles that we use for determining emoji-text convergence, including proximity, minimum mapping, and prosodic correspondence. It concludes with an overview of the system of emoji-text convergence, presenting the system network guiding the close textual analysis conducted on the social media corpora used in the book.

Social media is resplendent with a creative blend of non-standardised graphical resources such as images, memes, digital stickers, avatars and GIFs that extend beyond the rigid parameters of Unicode emoji character encoding. This chapter explores how emoji interact with other kinds of visual resources beyond language in social media posts such as graphicons. The chapter aims to give the reader a sense of how a social semiotic intermodal approach furnishes a flexible toolkit for an analyst to explore emoji’s relations with other modes. It primarily analyses the meanings made through combinations of emoji, language and GIFs in tweets. The analysis reveals how graphicons such as GIFs and digital stickers often realise a salient ‘New’ of the posts wherein they occur, and thus foreground interpersonal meaning.

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.

The chapter examines the work of a composer Jean-Louis Florentz, whose work has perhaps a greater affinity to that of Messiaen than works by the more well-known triumvirate of spectralists (Grisey, Murail, and Levinas). Florentz’s works are distinguished by their originality and are notable for their use of world music, in particular Ethiopian liturgical music. The study evaluates the connections between the two men, the proximity and distance of their techniques, their musical aesthetics, and the spiritual approaches of these composers.

Chapter 1 presents the purpose of the book – i.e. describing how a text-based description of three world languages can be developed. The Systemic Functional Linguistic theory informing these descpriptons is introduced, including modellng of context and discourse semantics,and the basic theoretical parameters of metafunciton, rank and stratification.The nature argumentation in relation to grammar description is outlined.

Chapter 6 explores theme and information systems and structures. It concentrates on the need to argue from discourse semantics as far as the interpretation of information flow is concerned. This chapter brings some phonological analysis into the picture, since information systems are realised through prosodic phonology (i.e. rhythm and intonation). This work draws on Halliday’s analysis of English intonation, as presented in Halliday (1967, 1970) and Halliday & Greaves (2008).

This chapter focuses on the power of words and images. It introduces basic concepts that are pivotal in verbal, visual, and multimodal communication. First, it discusses writing in the digital age and explores the media linguistic mindset that is required in rapidly changing digital environments. Furthermore, a set of sixteen key practices of focused writing and writing-by-the way in the newsroom and beyond are presented. The second part of the chapter covers theoretical concepts of visual communication by addressing different approaches to reading images. One pivotal approach is social semiotics – a grand theory that can be applied to all kinds of semiotic material used for communication. This approach is complemented with concepts from other semiotic traditions as well as rhetorical and critical theories about images and their effects on the users. In addition, certain questions related to multimodal communication and related key concepts are discussed. The chapter concludes with the main message that all forms of human communication are multimodal.

This chapter concerns the early modern redefinition of psychology as the science of mind. It examines the way the “invention of mind” was incorporated into Descartes’s metaphysical project. This Cartesian innovation marked a rupture from the traditional science of the soul as a division of natural science or physics. Rejecting the Aristotelian partition of the soul into distinct powers and the Scholastic view of the principle of thought (the intellect) as only the highest psychic power, the new Cartesian psychology required the unity of the soul as the thinking substance. What constituted early modern psychology as a metaphysical science of mind, this chapter argues, was fundamentally Descartes’s “realist” thesis that mind is a thing (res). Together with this Cartesian substantialist view, its critical reception structured the modern science of mind. The early modern alternatives to Descartes’s ontological thesis about mind, the chapter highlights, were based either on the argument that mind is not a thing or on the argument that mind is a non-substantial thing, a mere mode. The chapter illustrates the first argument with Hobbes, the second with Regius and Spinoza.

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.

This chapter is the first of three that set out the basic building blocks of musical syntax in Renaissance music, beginning with those connected to pitch. The first section sets out the key concepts of music theory dating back to the time of Guido of Arezzo in the eleventh century, whose pertinence endures into the Renaissance (thus, the gamut, mode, the species of fourth and fifth, the so-called Guidonian Hand, and the hexachord). The next section lays out the complex (and at time fraught) relationship between these concepts and composed polyphony, laying bare in particular the tension between modes (which were initially adapted from Greek theory to classify plainchant) and polyphony. This is seen most obviously in the functioning of the most fundamental element of counterpoint, the cadence. The chapter concludes by considering other key elements of pitch-treatment, including musica ficta, dissonance treamtment, and enhanced or expanded chromatic practice.

The discussion of cadence in Chapter 4 leads to a consideration of voice-names, ranges, and functions as key compositional and stylistic determinants. The discantus/tenor relationship constitutes polyphony’s fundamental framework; the nomenclature, ranges, and functions of the voices surrounding it condition the evolution of musical style during the Renaissance. This chapter traces the changes in these parameters to c.1600, showing their audible impact on musical style. At their heart are two fundamental shifts, the first from a texture comprising two registral tiers in the early fifteenth century to the three-tier setup first introduced to continental polyphony c.1440 with the dissemination of the English ‘Missa Caput’, and the second during the last quarter of the century with the emergence of a four-voice texture with a separate range for each voice. The stylistic implications of these devopments are considered in detail, continuing into the next century with the stabilization of the handling of texture into a typology of mode, range, and polyphony, independent of the number of voices present.

Chapter 5 is mainly devoted to the interaction between waves and immersed bodies. In general, an immersed body may oscillate in six different modes, three translating modes (surge, sway, heave) and three rotating modes (roll, pitch, yaw). An oscillating body radiates waves, and an incident wave may induce a corresponding excitation force for each one of the six modes. When a body oscillates, it radiates waves. Such radiated waves and excitation forces are related by so-called reciprocity relationships. Such relations are derived not only for a single oscillating body but even for a group (or 'array') of immersed bodies. Axisymmeric bodies and two-dimensional bodies are discussed in separate sections of the chapter. Although most of this chapter discusses wave-body dynamics in the frequency domain, a final section treats an immersed body in the time domain.

Chapter 8 concerns a group of WEC units that may be realised in a more distant future, namely groups or arrays of individual WEC units and two-dimensional WEC units, which needs to be rather big structures. Firstly, a group of WEC bodies is analysed. Next a group consisting of WEC bodies as well as OWCs is analysed. Then the previous real radiation resistance needs to be replaced by a complex radiation damping matrix which is complex, but Hermitian, which means that its eigenvalues are real.

The first part of Chapter 7 deals with oscillating water columns (OWCs). The concepts of radiation conductance and susceptance are introduced. The former is related to the radiated power, whereas the latter represents the reactive power. Expressions for the power absorbed by the OWC are derived, which are analogous to those of the oscillating body WEC. The potential energy of the OWC is also discussed. The last part of Chapter 7 deals with wave energy converters that move in modes other than the six conventional rigid-body modes. The theory of generalised modes are described, and some examples are given to illustrate the utility of the theory.

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.