Quiz 5 · Tables, Graphs, and Charts — Ancient America to the Singularity

Who made this?

1. Who made it?: The page in the photograph, folio 47r, was painted about 1541 in Mexico City by Mexica scribes, twenty years after the conquest. Their names are not recorded. A Spanish priest who spoke Nahuatl wrote notes beside the pictures; the book was made at the order of Antonio de Mendoza, the first viceroy, as a report for the king of Spain, and it carries the viceroy’s name, not the painters’.
2. When, and where?: About 1541, on European paper, in what had been Tenochtitlan. The tribute pages copy an older Mexica record, the Matrícula de Tributos, painted before the conquest and kept today in Mexico City. The painters were working in a counting system their people had used for centuries: a flag above an object means twenty of them, a feather means four hundred, a pouch means eight thousand.
3. Why, and for whom?: To show the king what each province of the empire had sent to Tenochtitlan every year: cloaks by the hundred, warrior suits and shields, bins of maize and beans, cacao, feathers, gold dust, honey. Each page is a table. Down the side are the towns that paid; across the page are the goods, each with its counting sign. It was a record of power, and a bill.
4. Who has it now, and how did it get there?: The Bodleian Library at Oxford, since 1659, where it is the first manuscript in the catalogue of John Selden’s books. It never reached the king. The usual story, first told by a later owner, is that the ship carrying it was taken by French privateers; what is certain is that a French cosmographer, André Thevet, wrote his name in it in 1553, that Richard Hakluyt bought it in France and carried it to England, and that it passed through Samuel Purchas to Selden and the Bodleian, where it sat uncatalogued for about 170 years. Scholars found it again in the 1830s. The library has put every page online, free to view.
5. Whose voice is missing here, and where can we hear it?: The painters’, in the pictures, and the priest’s, in the Spanish notes, which sometimes explain and sometimes get things wrong. The numbers speak the Mexica language of counting, which is the subject of Quiz 10. A reader of this page is reading two hands at once.

For your notebook: a table made for a king who never saw it, by painters whose people had been counting this way long before his grandfather was born. Whose table is it?

Sources: Bodleian Library, Digital Bodleian, “Codex Mendoza, MS. Arch. Selden. A. 1”; INAH, Códice Mendoza digital edition (2014); Frances Berdan and Patricia Anawalt, The Codex Mendoza (1992); Daniela Bleichmar, “Codex Mendoza,” in New World Objects of Knowledge (2021).

First, the idea

A table is numbers in rows and columns. A graph is a picture of a table. The test will give you both and ask you to find a value, compare two values, spot a trend, do a small calculation, or decide which conclusion the numbers support. Most mistakes on these questions are not arithmetic. They come from not reading the edges of the figure before reading the middle.

The title says what is being counted and when. The headings say what each column holds. The units say what one means: one person, one thousand people, one percent. A table marked “in thousands” with 299 in a cell means 299,000. The axis of a graph is its ruler; read where it starts and what each tick is worth.

A bar is a flag. The Mexica scribe who drew a flag over a bundle of cloaks meant twenty cloaks, and a feather meant four hundred; the reader had to know what the sign was worth before the picture meant anything. A bar graph works the same way with length. Before you read a bar, read what one unit of it is worth. The axis is the flag.

Three kinds of graph come up. A bar graph compares amounts; the eye can see at once that one bar is twice another. A line graph shows change over time; read its slope. A circle graph shows parts of a whole; the whole circle is always 100 percent of something, and the question to ask is, 100 percent of what.

That last question is the trap that catches the most people. Percent of what? Six percent of all Mexicans speak an Indigenous language. Twenty-two percent of Indigenous-language speakers speak Náhuatl. Both are true; they have different wholes. And a share can fall while a number rises: if the country grows faster than the group, the group’s percent goes down even as more people join it. When the test says “percent,” find the whole before you find the part.

Worked example — thinking out loud

Two examples, one from the tribute roll and one from the test’s kind of figure, because they are the same skill.

A page of the roll shows a bundle of cloaks with a feather sign above it, and a shield with a flag above it. How many of each? I want to count the cloaks in the picture, but the picture shows one bundle. The sign above it is the number: a feather is four hundred, so four hundred cloaks. A flag is twenty, so twenty shields. The object tells me what; the sign tells me how many. If I did not know the signs, the page would be a row of drawings and nothing else.

Two rows, printed for this example
Language	Speakers, 2020
Náhuatl	1,651,958
Maya	774,755

The question: which has about half as many speakers as the other? Half sounds like an eyeball judgment, but a table lets me check it exactly: 774,755 doubled is 1,549,510, a little under 1,651,958. So Maya has a little less than half, and “about half” is a fair answer while “exactly half” would be wrong. In Part B these same numbers come back as a bar graph, where your eye can make this comparison in one glance and the table stands by for the checking. The graph is for seeing; the table is for proving.

☞ Connects. Behind: Quiz 3 (reading the legend before the map). Ahead: Quiz 10 (Mexica and Maya counting, where the flag and the feather come back), Quiz 42 (the Great Depression in graphs), Quiz 45 (economic data on the test). The language table returns in Quiz 31 and Quiz 60.

Part A · The skill by itself

1. Read the table, including its heading.

Speakers of two languages, 2020
Language	Speakers (in thousands)
Otomí	299
Totonaco	256

According to the table, how many people spoke Totonaco in 2020?

256 2,560 256,000 2,560,000

2. In Mexico’s 1930 census, about 2.3 million people spoke an Indigenous language, about 16 percent of the population. In 2020, about 7.4 million did, about 6 percent of the population. Which statement do these numbers support?

Fewer people spoke an Indigenous language in 2020 than in 1930. The number of speakers rose while their share of the population fell. The share of speakers rose while their number fell. Mexico’s population shrank between 1930 and 2020.

3. Read the circle graph.

The whole circle stands for

all speakers of Indigenous languages in Mexico all people in Mexico aged 3 and over all speakers of Náhuatl all people in the Americas

Part B · The skill in the wild

A table and a bar graph of the same numbers, from Mexico’s 2020 census. Read the title, the headings, and the axis before the questions. Note that the table’s last row is the total for all 68 Indigenous languages, not just the six listed.

Speakers of the six most-spoken Indigenous languages in Mexico, 2020 (people aged 3 and over)
Language	Speakers	Share of all Indigenous-language speakers
Náhuatl	1,651,958	22.4%
Maya	774,755	10.5%
Tseltal	589,144	8.0%
Tsotsil	550,274	7.5%
Mixteco	526,593	7.2%
Zapoteco	490,845	6.7%
All 68 Indigenous languages	7,364,645	100%

Drawn to scale from the table. Reading the bars: Náhuatl’s bar is about twice Maya’s and about three times Tsotsil’s.

Source: INEGI, Censo de Población y Vivienda 2020, population aged 3 and over; the six languages’ shares as published by INEGI and Inmujeres. Mexico recognizes 68 Indigenous languages. The 7.4 million speakers were about 6 percent of the country’s people.

4. According to the table, how many people spoke Tseltal in 2020?

550,274 589,144 774,755 8.0

5. About how many more people spoke Náhuatl than Maya?

about 230,000 about 880,000 about 2.4 million about 12 percent

6. On the bar graph, the Tsotsil bar is about what fraction of the Náhuatl bar?

one half one third one quarter one tenth

7. Which statement do the table and graph support?

Most people in Mexico speak an Indigenous language. Náhuatl has more speakers than Maya and Tseltal combined. The six languages listed are spoken by most of Mexico’s people. Fewer than 400,000 people speak Zapoteco.

8. Complete the sentence so that it matches the figures.

The table gives [rough guesses / exact counts / percentages only], and the bar graph makes comparisons easy to see; together, the six languages listed were spoken by [about 6 percent / about 62 percent / about 100 percent] of all Indigenous-language speakers in Mexico.

The key — and why the tempting answers tempt

1. C. The heading says “in thousands,” so 256 means 256,000. A is the cell read without its heading, the single most common table error on the test. B and D add zeros to the wrong place.

2. B. 2.3 million grew to 7.4 million, so the number rose. Sixteen percent fell to six, so the share fell. Both at once, because the country grew faster than the group. A reads the falling percent as a falling number. C reverses both. D is the opposite of what the numbers imply: a group can triple and still shrink as a share only if the whole grew even more.

3. B. The label under the graph says so: people in Mexico aged 3 and over. Six percent of that whole speak an Indigenous language. A is the small wedge, not the circle. A circle graph always shows parts of one whole; find the whole first.

4. B. Straight from the Tseltal row. A is the Tsotsil row, one line down, an easy slip between two similar names. C is Maya. D is Tseltal’s share, a percent, not a count: the column heading tells you which is which.

5. B. 1,651,958 − 774,755 = 877,203, about 880,000. On the graph, the gap between the two bars is a little more than the Maya bar itself. A is the gap between Maya and Tsotsil. C adds instead of subtracting. D answers in percent when the question asked how many people; 22.4 minus 10.5 is 11.9 points of share, which is a different fact.

6. B. 550,274 is almost exactly one third of 1,651,958. On the graph the Tsotsil bar ends just past the 500 tick and the Náhuatl bar past 1,650. A is Maya’s fraction, not Tsotsil’s. C and D come from eyeballing without the ticks; the axis is the flag.

7. B. 774,755 + 589,144 = 1,363,899, which is less than 1,651,958. A confuses 6 percent of Mexico with a majority. C confuses 62 percent of Indigenous-language speakers with 62 percent of the country. D: Zapoteco is 490,845, more than 400,000. Three of the four wrong answers here are “percent of what” mistakes.

8. exact counts; about 62 percent. The table’s second column is counts to the last person. The shares in the third column add to 62.3 percent. “About 6 percent” is the share of all Mexicans, a different whole. “About 100 percent” forgets the other 62 languages in the total row. The whole circle, again: 100 percent of what.

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