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DATA REPRESENTATION
Graphics are a concise and organized way of presenting information. Once you realize that all graphics have
some common basic elements, it will not matter whether the information presented in them is in the area of
biology, chemistry, earth and space science, physics, or even bubble gum sales.
Consider the following train schedule:
A.M. A.M. A.M. A.M. P.M. P.M. P.M. P.M.
Congers Station 12:21 3:20 6:19 9:19 12:19 3:19 6:19 9:19
New City 12:32 3:30 6:30 9:30 12:30 3:30 6:30 9:30
Valley Cottage 12:39 3:37 6:37 9:37 12:37 3:37 6:37 9:37
Nyack 12:48 3:45 6:46 9:46 12:46 3:46 6:46 9:46
West Nyack 12:53 3:53 6:54 9:54 12:54 3:54 6:54 9:54
Bardonia 1:06 4:03 7:05 10:05 1:05 4:05 7:05 10:05
By looking at the table, you can determine:
■
the times the trains leave Congers Station (12:21 A.M., 3:20 A.M., 6:19 A.M., 9:19 A.M., 12:19 P.M., 3:19
P.
M., 6:19
P.M., and 9:19 P.M.).
■
the times they get to West Nyack (12:53 A.M., 3:53 A.M., 6:54 A.M., 9:54 P.M., 12:54 P.M., 3:54 P.M., 6:54
P.M., and 9:54 P.M.).
■
how often the trains run (about every 3 hours).
■
how long it takes the train to get from New City to Valley Cottage (7 minutes).
Imagine how many lines of text would be required to describe this schedule without using a table, and
how much more confusing and complicated it would be for a passenger to get the basic information in the
examples above. The point is that tables, graphs, charts, figures, and diagrams are useful and without realiz-
ing it, you analyze graphical information on a daily basis.
The only difference between these everyday encounters of graphical information and the ACT is that
on this test the information in the graphics will be of a scientific nature and you may run into words or con-

cepts you have never heard of before. But just because you don’t know what a diffusion coefficient, a refrac-
tive index, or a stem cell is, it doesn’t mean that you won’t be able to analyze graphical information in which
these unfamiliar concepts are mentioned. Did you need to know where Bardonia is to analyze the train sched-
ule above? No. All you did was realize that each row (horizontal) listed the times at which the trains arrive at
that station, and that each column (vertical) listed the times at which one train that left Congers Station would
arrive at other stations on the way to Bardonia.
You see? You don’t need an amazing science vocabulary to do well on the ACT. In fact, using informa-
tion not presented in the exam question could harm you, since test instructions tell you to only use what you
are given. Going back to our train schedule example, if you happen to live on the Bardonia line, you may know
that the trains on that line leave every 30 minutes (not every 3 hours) during the day. But if the schedule were
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on the exam, and you were asked how often the train runs, based on the information provided, your answer
would be marked wrong if you answered that it runs every 30 minutes.
In the following sections, you will learn to recognize the common elements and trends in information
presented in graphical form. You will also read some suggestions on approaching the types of graphical rep-
resentation questions that often appear on the ACT.
Table Basics
All tables are composed of rows (horizontal) and columns (vertical). Entries in a single row of a table usu-
ally have something in common, and so do entries in a single column. Look at the table below that lists the
thermal conductivities (in Watts per meter Kelvin) as a function of temperature (in Kelvin).
TEMPERATURE [K]
ELEMENT 100 200 300 400 500 600
Aluminum 300 237 273 240 237 232
Copper 483 413 309 392 388 383
Gold 345 327 315 312 309 304
Iron 132 94 80 69 61 55
Platinum 79 75 73 72 72 72
You only need the table to answer the following questions.
1. Which one of the metals listed has the highest thermal conductivity at 300 K?

2. At what temperature does gold have the lowest thermal conductivity?
3. How does the thermal conductivity for aluminum change in the range of temperatures given?
To answer question number one, you would look at the column that lists the thermal conductivities at
300 K. You would see that the highest number in that column is 398. You would place your finger on that
number and use the finger as a guide across the row, all the way to the left to see which metal has a conduc-
tivity of 398 watts per meter Kelvin. And you would see that the row you selected lists the thermal conduc-
tivities of copper.
Question number two is very similar to question number one, but now you are asked to find the max-
imum number in a row (gold), and determine to which column it corresponds. In the row listing the ther-
mal conductivities of gold, the highest number is 345. Put your finger on it and use it as a guide, straight to
the top of that column to see that the thermal conductivity of gold is at the maximum at 100 K.
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In question three, you are asked to describe a trend. This is another common question type. Is there a
change? Do the numbers increase? Decrease? Randomly change (no trend)? Looking at the row of data for
aluminum, you can conclude that the thermal conductivity for this metal first increases, and then between
300 K and 400 K, it begins to decrease.
Graph Basics
The most common types of graphs are scatter plots, bar graphs, and pie graphs. What follows is an explana-
tion of each, with examples you can use for practice.
SCATTER PLOTS
Whenever a variable depends continuously on another variable, this dependence can be visually represented
in a scatter plot. Examples include a change in a property or an event as a function of time (population
growth) and change in a property as a function of temperature (density). A scatter plot consists of the hor-
izontal (x) axis, the vertical (y) axis, and collected data points for variable y, measured at variable x. The vari-
able points are often connected with a line or a curve. A graph often contains a legend, especially if there is
more then one data set or more than one variable. A legend is a key for interpreting the graph. Much like a
legend on a map lists the symbols used to label an interstate highway, a railroad line, or a city, a legend for a
graph lists the symbols used to label a particular data set. Look at the sample graph above. The essential ele-
ments of the graph—the x- and y-axis—are labeled. The legend to the right of the graph shows that dots are

used to represent the variable points in data set 1, while squares are used to represent the variable points in
data set 2. If only one data set exists, the use of a legend is not essential.
Now let’s see how we can answer graphical representation questions effectively by understanding and
analyzing the information presented in a graph. Look at the example below.
Graph Title
100
120
140
80
60
40
20
0
0246810
data set 1
data set 2
Y-Axis
X-Axis
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The variable on the x-axis is the wavelength. The index of refraction of water is the variable on the y-axis.
The thick black line connects the data points collected by measuring the index of refraction at different wave-
lengths.
What can you tell about the index of refraction of water from the graph above? For one, you can get an
estimate of the refractive index at a particular wavelength. How would you find the index of refraction at a
wavelength of 500 nm? First, find 500 nm on the horizontal x-axis. But there is no 500 nm! Sure, 500 nm is
not explicitly labeled, but you can expect it to be exactly between 400 nm and 600 nm, which are labeled.
There are four grid divisions between 400 and 600, so each division corresponds to a 50 nm increment. Once
you locate 500 nm, put your finger on it to use as a guide. Move it up along the gridline until it meets the thick
black line connecting the data points. Now, determine the index of refraction that corresponds to that wave-

length by carefully guiding your finger from the point where the 500 nm gridline crosses the data curve to
the vertical y-axis, all the way on the left. The refractive index of water at 500 nm is almost 1.34.
By looking at the graph, you can also say that the index of refraction of water ranges from 1.32 to 1.4.
What can you say about the trend? How does the index of refraction vary with increasing wavelength? It first
rapidly decreases, and then slowly levels off around 1.32. For practice, try to look for scatter plots with dif-
ferent trends—including:
■
increase
■
decrease
■
rapid increase, followed by leveling off
■
slow increase, followed by rapid increase
■
rise to a maximum, followed by a decrease
■
rapid decrease, followed by leveling off (as in the wavelength example)
■
slow decrease, followed by rapid decrease
■
decrease to a minimum, followed by a rise
■
predictable fluctuation (periodic change, such as a light wave)
■
random fluctuation (irregular change)
Index of Refraction of Water at 20°C
as a Function of Wavelength
1.4
1.42

1.38
1.36
1.34
1.32
1.3
0 200 400 600 800 1000 1200
1400
index of refraction
wavelength [nm]
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Do you see how you didn’t need to know a thing about refraction to understand the graph?
There are also graphs on which several different variables are plotted against a common variable. See
the following chart with levels of three different hormones in the female body (FSH, LH, and progesterone)
throughout the menstrual cycle.
Here, there are three different sets of data, one set for each hormone. Different sets are labeled using dif-
ferent symbols for data points—a circle for FSH, a triangle for LH, and a square for progesterone, as shown
in the legend in the top right corner of the graph.
Using this graph you can determine the concentration of a particular hormone on a particular day in
the cycle. For example, the concentration of FSH on day 12 of the cycle is about 20 units per ml. To obtain
this answer, first find the data line that corresponds to FSH, and then locate the point at which day 12 grid-
line intersects the FSH line. Finally, slide your finger from the point of intersection to the y-axis, and read the
corresponding concentration.
You can also use the graph to make general statements about the change of hormone concentrations
throughout the cycle. For example, the concentration of LH is highest around the day 13 of the cycle. Using
the graph, you can also compare the concentrations of different hormones on the same day. For example, the
concentration of progesterone is higher than the concentration of FSH on day 21 of the menstrual cycle.
BAR GRAPHS
Bar graphs are similar to scatter plots. Both have a variable y plotted against a variable x. However, in bar
graphs, data are represented by bars, rather than by points connected with a line. Bar graphs are often used

to indicate an amount or level, as opposed to a continuous change. Consider the bar graph on the next page.
It illustrates the prevalence of hypertension among different age groups.
70
80
60
50
40
30
20
10
0
0246810121416182022242628
FSH
LH
Progesterone
Hormone concentration [units per ml]
Da
y
of menstrual c
y
cle
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You could immediately see that hypertension is more prevalent in older age groups. You could also say
that at the prevalence of hypertension in the 45–54 age group (more than 40%) exceeds the average preva-
lence among all age groups (30%). This graph could have been packed with more information. It could have
included the hypertension prevalence among men and women. In that case, there would be three bars for each
age group, and each bar would be labeled (for men, women, and both sexes) by using a different shading pat-
tern, for example.
Some bar graphs have horizontal bars, rather than vertical bars. Don’t be alarmed if you see them on

the ACT.You could analyze them using the same skills you would for analyzing a bar graph with vertical bars.
PIE GRAPHS
Pie graphs are often used to show what percent of a total is taken up by different components of that whole.
The pie chart below illustrates the relative productivity (new plant material produced in one year) of differ-
ent biomes (desert, tundra, etc.).
Relative Productivity
of Biomes
Desert
1%
Tundra
2%
Chaparral
11%
Grassland
9%
Taiga
12%
Savanna
14%
Temperate
deciduous
forest
18%
Tropical
rain
forest
33%
Hypertension among Different
Age Groups
50

70
60
40
30
20
10
0
all ages 18–24 25–34 35–44 45–54 55–64 65–74
Prevalence of
hypertension (%)
Age group
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