As the number of people using quantitative methods to study "cultural data" is gradually increasing (right now these people work in a few areas which do not interact: digital humanities, empirical film studies, computers and art history, computational social science), it is important to ask: what is statistics, and what does it mean to use statistical methods to study culture? Without the reference to mathematics, this description looks very friendly - there is nothing here which directly calls for positivism, or scientific method. But of course this is not enough to argue that statistics and humanities are compatible projects. Examples of descriptive statistics are mean (the measure of central tendency) and standard deviation (the measure of dispersion). Application of descriptive statistics does not have to be followed by inferential statistics.
Accordingly, the current explanation of descriptive statistics on Wikipedia includes both numbers and graphs: "Descriptive statistics provides simple summaries about the sample and about the observations that have been made. What we get from this is that we don't have to do statistics with numbers - visualizations are equally valid.
Francis Galton’s first correlation diagram, showing the relation between head circumference and height, 1886.
For example, we can summarize a text with numbers such as the average sentence length, the proportion between nouns and verbs, and so on. In the previous examples, the algoritms extracted some words or phrases from a text and organized them visually - therefore it possible to argue that they still belong to graph method of descriptive statistics. In my lab, we have been developing free software tools for summarizing large image and video collections.
To summarize a complex image we can translate it into a monochrome version that only shows the key shapes.
There is nothing "positivist" or "scientific" about such same-media summaries, because they are what humanities and the arts have always been about. Until development of statistics in the 19th century, all kinds of summaries were produced manually.

I don't think that we can find some hard definite threshold which will separate summaries which can only be produced by algorithms (because of the data size) from the ones produced by humans. I don't know if my arguments will help us when we are criticized by people who keep insisting on a wrong chain of substitutions: digital humanities=statistics=science=bad. Since the 1970, computers gradually made the use of graphs for studying the data (as opposed to only illustrating the findings) equally important.
Source: Michael Friendly and Daniel Danis, The Early Origins and Development of the Scatterplot. We can also use graphs: for example, a bar chart that shows frequency of all words used in the text in ascending order.
It summarizes a text by showing us most frequently used words that are scaled in size according to how often they are used.
In some of our applications, the whole collection is translated into a single high-resolution visualization (so these are not summaries) but in others, a sample of an image set, or parts of the images are used as the summaries. For example, modernity and industrialization were often summarized by images of planes, cars, gear, workers, and so on. Art images always summarized visible or imaginary reality by representing only some essential details (like contours) and omitting others. Statistics "industrializes" this process, substituting subjective summarization by the objective and standardized measures.
Examples of such summaries are a number representing the average number of words per sentence in a text which has tens of thousands of sentences, or the graph showing relative frequencies of all the words appearing in a long text. In the 1970s, without the use of any computers, French film theorists advanced the idea that most classical Hollywood films follow a single narrative formula.
But if we keep explaining that statistics is not only about inferences and numbers, gradually we will be misunderstood less often. I will address their assumptions, their use in industry, and how in digital humanities we may use them differently in a future article).

This graph was a paet of many early statistical studies of Quetelet which led him to formulate a theory of "average man" (1835) which states that many measurements of human traits follow a normal curve. Descriptive statistics is only concerned with the data you have – it is a set of diverse techniques for summarizing the properties of this data in a compact form. The article suggests that this diagram was an intermediate form between a table of numbers and a true graph.
In this scenario, there is no translation of one media type into another type (for example, text translated into numbers or into graphs). It carries exactly the same information, as a graph which plots their frequencies - but if the latter foregrounds the graphic representation of the pattern, the former foregrounds the words themselves. For example, here is the visual summary of 4535 covers of Time magazine which uses one one pizel wide horizontal column from from each cover.
Today in TV commercials, a network society is typically summarized by a visualization showing a globe with animated curve connecting many points. While at first these were only summaries of numerical data, the development of computational linguistics, digital image processing, and GIS in the 20th century also automates production of summaries of media such as texts, images, and maps. This is just one example of countless "summaries" produced in all areas of humanities (whether they are accurate is a separate question). Although such summaries are not (or not yet) understood as belonging to statistics, they perfectly fit the definition of descriptive statistics. Tukey's work lead to the development of statistical and graphing software S, which in its turn lead to R, which today is the most widelly used computing platform for data exploration and analysis.

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