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YWho Was “A MOURNER”?

Who wrote the plays attributed to William Shakespeare? Which colonialpatriot penned the VINDEX essay in the January 8, 1770, issue of The

Boston Gazette and Country Journal? Who wrote the 12 contestedFederalist papers? Such questions about authorship of unattributed

documents are one of the many problems confronting historians. Sta-tistical analyses, when combined with other historical facts, often help

resolve these mysteries.One such historical conundrum is the identity of the writer

known simply as “A MOURNER.” A letter appeared in the February26, 1770, issue of The Boston Gazette and Country Journal. The text of theletter is as follows:

The general Sympathy and Concern for the Murder of the Lad by thebase and infamous Richardson on the 22d Instant, will be sufficientReason for your Notifying the Publick that he will be buried from hisFather’s House in Frogg Lane, opposite Liberty-Tree, on Monday next,when all the Friends of Liberty may have an Opportunity of payingtheir last Respects to the Remains of this little Hero and first Martyr tothe noble Cause—Whose manly Spirit (after this Accident happened)appear’d in his discreet Answers to his Doctor, his Thanks to the Cler-gymen who prayed with him, and Parents, and while he underwent thegreatest Distress of bodily Pain; and with which he met the King of Ter-rors. These Things, together with the several heroic Pieces found in hisPocket, particularly Wolfe’s Summit of human Glory, gives Reason tothink he had a martial Genius, and would have made a clever Man.

A MOURNER.

The “Lad” the writer refers to is Christopher Sider, an 11-year-old sonof a poor German immigrant. Young Sider was shot and killed on February22, 1770, in a civil disturbance involving schoolboys, patriot supporters ofthe nonimportation agreement, and champions of the English crown. Thisevent preceded the bloody Boston Massacre by just a couple of weeks. OfSider’s funeral, John Adams wrote, “My eyes never beheld such a funeral.The Procession extended further than can be well imagined.” (Diary ofJohn Adams entry for 1770. MONDAY FEB. 26 OR THEREABOUTS.)

From a historical perspective, the identity of “A MOURNER” remainsa mystery. However, it seems clear from the letter’s text that the author sup-ported the patriot position. This assumption somewhat narrows the field ofpossible writers.

Ordinarily, a statistical analysis of the frequencies of various words con-tained in the contested document, when compared with frequency analysesfor known authors, would permit an identity inference to be drawn. Unfor-tunately, in this case, the letter is too short for this strategy to be useful. An-other possibility is based upon the frequencies of word lengths. In thisinstance, a simple count of letters is generated for each word in the docu-ment. Proper names, numbers, abbreviations, and titles are removed fromconsideration, because these do not represent normal vocabulary use. Caremust be taken in choosing comparison texts, since colonial publishers habit-

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ually incorporated their own spellings into the essays they printed. There-fore, it is desirable to get comparison texts from the same printer the con-tested material came from.

The table below contains the summary analysis for six passages printedin The Boston Gazette, and Country Journal in early 1770. The Tom Sturdy(probably a pseudonym) text was included because of the use of the phrase“Friends of Liberty,” which appears in “A MOURNER”’s letter, as opposedto the more familiar “Sons of Liberty.” Alexander Hamilton, James Otis,and Samuel Adams are included because they are well-known patriots whofrequently wrote articles that were carried by the Boston papers. In the caseof Samuel Adams, the essay used in this analysis was signed VINDEX, oneof his many pseudonyms. The table presents three summaries of workpenned by Adams. The first two originate from two separate sections of theVINDEX essay. The last summary is a compilation of the first two.

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Summary Statistics of Word Length from Sample Passages by VariousPotential Authors of the Letter Signed “A MOURNER”

Tom Alexander James Samuel Samuel Samuel Sturdy Hancock Otis Adams-1 Adams-2 Adams-1&2

Mean 4.08 4.69 4.58 4.60 4.52 4.56

Median 4 4 4 3 4 4

Mode 2 3 2 2 2 2

Standard Deviation 2.17 2.60 2.75 2.89 2.70 2.80

Sample Variance 4.70 6.76 7.54 8.34 7.30 7.84

Range 13 9 14 12 16 16

Minimum 1 1 1 1 1 1

Maximum 14 10 15 13 17 17

Sum 795 568 842 810 682 1492

Count 195 121 184 176 151 327

1. Acting as a historical detective, generate a data set consisting of thelength of each word used in the letter signed by “A MOURNER.” Besure to disregard any text that uses proper names, numbers, abbrevia-tions, or titles.

2. Calculate the summary statistics for the letter’s word lengths. Compareyour findings with those of the known authors, and speculate about theidentity of “A MOURNER.”

3. Compare the two Adams summaries. Discuss the viability of word-length analysis as a tool for resolving disputed documents.

4. What other information would be useful to identify “A MOURNER”?

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What Car Should I Buy?

Suppose you were in the market to purchase a used car. In order to make aninformed decision regarding your purchase, you would need to collect asmuch information as possible. Among the information you might considerare the typical price of the car, the typical number of miles the car shouldhave, its crash test results, its insurance costs, and its expected repair costs.

1. Make a list of at least three cars that you would consider purchasing.Tobe fair, the cars should be in the same class (such as compact, midsize,and so on). They should also be of the same age.

2. Collect information regarding the three cars in your list by finding atleast eight cars of each type that are for sale. Obtain such informationas the asking price and the number of miles the car has. Sources of datainclude your local newspaper, classified ads, and car Web sites (such ashttp://www.cars.com/ and http://www.autobytel.com/). Compute sum-mary statistics for asking price, number of miles, and other variables ofinterest.

3. Go to the Insurance Institute for Highway Safety Web site,http://www.hwysafety.org. Select the Vehicle Ratings link. Choose themake and model for each car you are considering. Obtain informationregarding crash testing for each of the cars under consideration. Com-pare cars in the same class. How does each of your cars compare? Isone of the cars you are considering substantially safer than the others?What about repair costs? Compute summary statistics for crash testsand repair costs.

4. Obtain information about insurance costs. Contact various insurancecompanies to determine the cost of insuring the cars you are consider-ing. Compute summary statistics for insurance costs.

5. Write a report supporting your conclusion regarding which car youwould purchase.

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(d) Calculate the standard deviation of the weight ofwater collected for product B.

(e) Construct a stem and leaf diagram for these data.

Does there appear to be a difference in these twoproducts’ ability to mitigate water seepage? Why?

Note to Readers: In many cases, our test protocol and analyticalmethods are more complicated than described in these examples.The data and discussions have been modified to make the materialmore appropriate for the audience.

Weight of Collected Water

Product Replicate (in grams)

A 1 91.2

A 2 91.2

A 3 90.9

A 4 91.3

A 5 90.8

A 6 90.8

B 1 87.1

B 2 87.2

B 3 86.8

B 4 87.0

B 5 87.2

B 6 87.0

Basement Waterproofer Test Chamber

© 2002 by Consumers Union of U.S., Inc., Yonkers, NY 10703-1057, a nonprofit organization.Reprinted with permission from the June, 2002 issue of CONSUMER REPORTS® for educa-tional purposes only. No commercial use or photocopying permitted. To learn more aboutConsumers Union, log onto www.ConsumerReports.org <http://www.ConsumerReports.org>.

A waterproofing coating can be an inexpensive andeasy way to deal with leaking basements. But how ef-fective are they? In a recent study, Consumer Reports(June 2002) tested nine waterproofers to rate their ef-fectiveness in controlling water seepage though con-crete foundations.

In order to compare the products’ ability to con-trol water seepage, we applied two coats of each prod-uct to slabs cut from concrete block. For statisticalvalidity, this process was repeated at least six times. Ineach test run, four blocks (each coated with a differentproduct) were simultaneously placed in a rectangularaluminum chamber. See the picture below.

The chamber was sealed and filled with water andthe blocks were subjected to progressively increasinghydrostatic pressures. Water that leaked out duringeach period was channeled to the bottom of the cham-ber opening, collected and weighed.

The table on the right contains a subset of the datacollected for two of the products tested:

Using this data,

(a) Calculate the mean, median and mode weight ofwater collected for product A.

(b) Calculate the standard deviation of the weight ofwater collected for product A.

(c) Calculate the mean, median, and mode weight ofwater collected for product B.

Basement Waterproofing Coatings

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