snucongo.orgistics is the scientific research of illustration conclusions from data. This chapter introduces a rough taxonomy of information, and also devices for presenting, summarizing, and also displaying data: tables, frequency tables, histograms, and also percentiles. The tools are illustrated using datasets from profession key litigation and also geophysics.

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In its broadest sense, snucongo.orgistics is the scientific research of drawing conclusions about the world from information. Documents are monitorings (measurements) of some quantity or high quality of somepoint in the civilization. "Data" is a plural noun; the singular form is "datum." Our stays are filled via data: the weather, weights, prices, our snucongo.orge of health and wellness, exam qualities, financial institution balances, election results, and so on. Documents come in many creates, the majority of of which are numbers, or have the right to be interpreted right into numbers for analysis. In this chapter, we will see numerous kinds of information and also tools for summarizing data.

Tright here are several essential questions to keep in mind as soon as you evaluate quantitative evidence:

Are the data appropriate to the question asked? Do the information make sense?

The answers to these concerns are crucial to drawing conclusions from data.

Trident® sugarmuch less gum offered to advertise that "4 out of 5 dentistssurveyed recommend Trident® sugarmuch less gum for their patients that chew gum."

Such a survey claims little around whether Trident® gum is much better for yourteeth than other gum, with or without sugar.It would be even more relevant to research the effect on teeth of chewingdifferent kinds of gum, not the opinions of dentists who can not haveperformed (or even read) any kind of empirical study on the results of differentkinds of gum.

For more on these topics, watch Hooke (1983),Huff (1993) andTaleb (2007).


A variable is a value or characteristic that deserve to differ from individual to individual. Documents are primarily recorded values of variables. Quantitative variables take numerical values whose "size" is coherent. Quantitative variables answer concerns such as "exactly how many?" or "just how much?" For instance, it makes sense to add, to subtract, and also to compare two persons" weights, or two families" incomes: These are quantitative variables. Quantitative variables commonly have actually measurement systems, such as pounds, dollars, years, volts, gallons, megabytes, inches, degrees, miles per hour, pounds per square inch, BTUs, and so on.

Some variables, such as social defense numbers and zip codes, take numerical worths, yet are not quantitative: They are qualitative or categorical variables. The sum of 2 zip codes or social defense numbers is not systematic. The average of a list of zip codes is not meaningful. Qualitative and also categorical variables typically carry out not have actually devices. Qualitative or categorical variables—such as sex, hair color, or ethnicity—team individuals. Qualitative and categorical variables have actually neither a "size" nor, frequently, a herbal ordering to their worths. They answer inquiries such as "which kind?" The values categorical and also qualitative variables take are frequently adjectives (for instance, green, female, or tall). Arithmetic through qualitative variables generally does not make sense, even if the variables take numerical values. Categorical variables divide people into categories, such as gender, ethnicity, age group, or whether or not the individual finished high school.

Examples of qualitative, quantitative, and categorical variables


Hot/Warm/Cold Population density: low/medium/high Height: short/medium/tallUnder 5", 5"–6", Over 6"Slender/Average/Overweight Young/Middle-aged/Old Social class: lower/middle/top Family size: fewer than 3, 3–5, more than 5


Temperature: pleasant/unpleasantRural/Urban area endomorph/mesomorph/ectomorph Type of climate GenderEthnicityZip codeHair colorCounattempt of beginning


Temperature in °C Population density: civilization per square mile Height in inchesHeight in centimeters Body mass index (BMI)Period in secondsIncome in dollarsFamily size (#people)

The distinction in between these kinds of variables is rather blurry. For instance, we might team eras into categories such as under 5 years old, between 5 and 15, between 15 and also 25, in between 25 and 40, and over 40. Similarly, whether gender or climate types are qualitative or categorical variables is not clear-reduced. Generally, if tright here is an implicit ordering of the values the variable deserve to take (hot is warmer than warm, which is warmer than cold), tbelow is a tendency to contact a variable qualitative fairly than categorical; some people call such variables ordinal. It is widespread to code categorical and qualitative variables using numbers, for instance, 1 for male and 0 for female. The truth that a category is labeled with a number does not make the variable quantitative! The genuine worry is whether arithmetic and also other mathematical operations with the values provides feeling.

Individuals require not be people; for instance, we might be comparing microclimates in the San Francisco Bay Area, utilizing variables such as

yearly rainfall in inches (quantitative) annual number of sunny days (quantitative, discrete) A classification into "extremely foggy," "rather foggy," and also "sunny." (qualitative, ordinal) annual average temperature in levels Fahrenheit. (quantitative)

Similarly, the "individuals" could be a solitary "individual" at different times: A variable might be the price of a share of Microsoft stock at various times.

It is sometimes beneficial to divide quantitative variables better right into discrete and constant variables. (This department is occasionally fairly synthetic.) The collection of possible worths of a discrete variable is countable. Examples of discrete variables encompass periods measured to the nearemainder year, the number of human being in a family, and also stock prices on the New York Stock Exreadjust. In the initially 2 of these examples, the variable can take only some positive integers as worths. In all 3 examples, tbelow is a minimum spacing in between the possible values. Many discrete variables are choose this—they are "chunky." Variables that count things are constantly discrete.

Examples of consistent variables include points prefer the specific periods or heights of individuals, the exact temperature of something, etc. Tright here is no minimum spacing between the feasible values of a consistent variable. The possible worths of discrete variables don"t necessarily have actually a minimum spacing. (For example, the collection of fractions—rational numbers—is countable, but there is no minimum spacing between fractions.) One factor the distinction in between discrete and also consistent variables is somewhat vague is that in practice tbelow is always a limit to the precision via which we deserve to measure any variable. The limit depends on the instrument we usage to make the measurement, exactly how a lot time we require to make the measurement, and so on. For most objectives, the difference between continuous and also discrete variables is not essential.

The complying with exercise checks your understanding of the distinctions among kinds of variables. The exercise will tell you automatically whether you are ideal or wrong: Each question is complied with by an image. Initially, the image is a question note. If you answer the question effectively, the question mark is replaced by a examine note. If you answer the question erroneously, the question mark is replaced by an X. Once you attempt the exercise, you can see the correct answer by clicking the picture. Clicking the picture aacquire will certainly hide the answer. Clicking the Systems connect (when tright here is one) reveals a much more comprehensive answer.

Sample Documents Sets

Throughout this book, as we learn brand-new approaches we shall apply them to real-world data from service, demography, education, law, medicine, and also physics. Applying the methods to information will certainly aid us to understand the approaches and to recognize once the techniques are proper. The following sections introduce information we shall usage to illustrate and also to exercise creating and interpreting tables, frequency tables, histograms, and also percentiles.

Trade Secret Data

The first data collection is the Trade Secret File, which occurred from a lawsuit alleging the theft of a customer list. The names of the world and firms have been changed, but otherwise, the facts are declared as I understand them.

On 1 May 1995, two previous employees of WeeBee Hardware (WBH), a firm that sells computer system components to computer system assemblers and also retailers, opened up the doors of a brand-new agency, Weasell Drives (WD). One of the former employees had worked at WBH up to the day prior to WD opened up its doors; the other had quit working for WBH around 18 months previously. Both firms are in the greater San Francisco Bay Area.

From the moment WD began organization, it marketed essentially the very same kinds of computer system components that WBH did, greatly to previous customers of among the former employees, at basically the exact same prices and also through fundamentally the very same crmodify terms. Certainly, in the first 2 days WD remained in company, one of the former employees had dubbed the top dozen of her WBH accounts. In its first month of company, WD marketed around $1 million of equipment to former customers of WBH; that amount increased to about $2million per month in the course of a couple of months.

The principals of WBH sought an injunction versus WD to proccasion it from offering to customers of WBH, alleging that their customer list was a trade secret and also had been misappropriated by its previous employees.

It is well establiburned that a customer list deserve to qualify as a profession secret: It has actually economic worth, and also derives its value from not being mainly well-known. Customer lists have the right to be the product of years of soliciting new organization by proclaiming and "cold-calling" tens of hundreds of potential customers and winnowing that list dvery own to a couple of hundred or a couple of thousand also who actually perform buy the type of devices the firm sells, who will buy it from that firm, and who pay promptly. With knowledge of a firm"s list of customers, a competitor can prevent the moment and also price of some heralding, cold-calling, checking credit recommendations, poor debt, and so on.

In response to WBH"s research for an injunction, WD asserted:

They found the names of the customers in public resources, such as CD-ROMs that contain lists of businesses, and also from computer magazines in which those customers advertise, not from their knowledge of WBH"s customers. Such a large overlap with WBH"s customer list was unavoidable, bereason WBH had actually so many kind of customers.

A The golden snucongo.orge Court of Appeals decision (ABBA Rubber Co. v. Seaquist 286 Cal. Rptr. at 528) develops that a "readily ascertainable by correct means" affirmative defense to a case of misappropriation is proper under specific circumstances:

f the defendants have the right to convince the finder of truth … (1) that it is a virtual certainty that anyone that manufactures specific types of commodities supplies rubber rollers, (2) that the manufacturers of those commodities are quickly identifiable, and (3) that the defendants" knowledge of the plaintiff"s customers resulted from that identification process and also not from the plaintiff"s records, then the defendants may create a defense to the misappropriation case.

ABBA Rubber Co., 286 Cal. Rptr. at 529, ftnt. 9.

WD would for this reason be in the clear if they can show that they established the customers they called from the CD-ROMs and/or magazines without utilizing their understanding of WBH"s customer list. I was maintained as an expert witness to calculate the probability that particular subsets of WD customers would certainly overlap with analogous subsets of the active WBH customer list to the level that they carry out, and also that WD would location as huge a number of calls to WBH customers as they did, under various assumptions. The plaintiff"s legislation firm matched the defendants" customer list versus the plaintiff"s, and versus advertisements in the magazines from which WD declared they obtained a lot of of their customers. The plaintiff agreed (stipulated) that fundamentally all the names in question were in the CD-ROMs. The plaintiff"s regulation firm likewise went with the defendants" telephone records and figured out calls to WBH customers and others. Only neighborhood toll calls and also long distance calls cause telephone documents, so calls to WBH customers that are close to WD might not be determined.

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WBH had actually 3310 active customers at the time in question; WD had actually 132. They had actually 93 customers in common. WD claimed to have actually discovered the names of 27 of their customers in local trade magazine advertisements, and also to have actually discovered the names of 31 of their customers in the CD-ROMs. A complete of 469 potential buyers of the kind of devices WD sells advertised in the magazines in question; 152 of them were WBH customers. Of the 27 customers WD claimed to have actually uncovered in the magazines, 26 were customers of WBH. Of the 31 customers WD asserted to have discovered in the CD-ROMs, 22 were customers of WBH. Of the 3310 WBH customers, 1769 were exterior the San Francisco Bay Area. Of the 132 WD customers, 8 were external the San Francisco Bay Area. All 8 of the WD customers outside the Bay Area were additionally customers of WBH. Other professionals estimated that tright here were even more than 90,000 potential buyers of the kinds of tools WBH and also WD sell in the UNITED snucongo.orgE all at once, and also even more than 60,000 outside the San Francisco Bay Area (including Silicon Valley). There were 2906 WBH customers to whom calls by WD would certainly have brought about phone records, and 68 WD customers for whom tright here were phone documents, of whom 53 were customers of WBH. In the month of May, 1995, WD inserted a full of 1050 calls that developed phone records, and 1006 of them were to the 53 customers of WBH.

Presenting the data in a narrative is very tough to follow. It is much less complicated to understand also the information making use of a table: