To make sense of the past, historians try to identify patterns in the evidence they collect. They look for connections between events or between various circumstances surrounding a single event. They try to determine what changed versus what stayed the same over time. At their most ambitious, they search for an underlying logic that explains historical trends, historical disjunctures (such as political and technological revolutions), and— ultimately—the dynamics of human behavior. Otherwise history would be just "one damn fact after another."

Quantitative historians use a wide variety of tools to help them locate patterns amid a welter of data. Some of these tools you are most likely familiar with from your grade school days, and we will start with them. You may be pleased to discover how much you already know about quantitative methods that will prove useful in your study of American history.

Let us begin with totals. Just tracking the total number of people in a particular place over time can be revealing. For example, using federal census records, we can determine how many people resided in New York City at ten-year intervals between 1790 and 1840. Indeed, the census takers themselves did the necessary addition, and the government published the results: in 1790, there were 33,131 residents; in 1800, there were 60,489; in 1810, there were 96,373; in 1820, there were 123,706; in 1830, there were 197,112; and in 1840, 312, 710. Written out in a single sentence, these numbers may not mean much. But if you put them in a table, you should begin to see a pattern.

Table A: The Population of New York City, 1790-1840

Year	Population
1790	33,131
1800	60,489
1810	96,373
1820	123,704
1830	197,112
1840	312,710

Looking at these totals, what do you think was the pattern of growth in the population of New York City from 1790 to 1840?

Downward
Upward
Flat

This graph makes the pattern even clearer:

Graph 1: The Population of New York City, 1790-1840

Reading this graph, in which decade do you think the most rapid growth in population occurred?

1830 and 1840
1810 and 1820
1800 and 1810
1790 and 1800

How can that be? Graph 1 illustrates the pattern of population growth by decade in absolute terms. You must still "read" the patterns carefully, however. It is tempting to conclude from Graph 1 not only that the population of New York City grew substantially between 1790 and 1840, but that it grew at a higher rate after 1820 because the line on the graph rises more steeply after 1820 than before.

Now look at Table B. If you calculate population growth per decade as a percentage of the city’s population at the start of the decade, you may be surprised by the results: by this measure, the decade with the highest rate of growth was 1790-1800.

Table B: The Rate of Population Growth by Decade, New York City, 1790-1840

Year	Population	Population growth over decade (absolute difference)	Rate of population growth (increase as percentage of population at decade's start)
1790	33,131
1800	60,489	27,358	83%
1810	96,373	35,884	59%
1820	123,704	27,331	28%
1830	197,112	73,408	59%
1840	312,710	115,598	59%

Graph 2: The Rate of Population Growth by Decade, New York City, 1790-1840

Graph 2 visually illustrates the change in the rate of population growth by decade. So what can we learn from Graph 2? By itself, it suggests that New York City’s population increased continuously between 1790 and 1840, but not at a consistent pace. While the population grew at virtually the same rate (59%) in each of three decades (1800 to 1810, 1820 to 1830, and 1830 to 1840), it grew at a noticeably higher rate in the 1790s and a markedly lower rate in 1810s. Why? Neither Graph 2 nor Table B provides an explanation, but were we to carry our study of New York City forward, we would want to investigate what was distinctive about the two "abnormal" decades.