# Data Representation Passages

Reading graphs is like reading in a foreign language. It comes easily to some and is very difficult for others. If you struggle with understanding graph, tables, and other visuals for ACT Science questions, this chapter containing tips, strategies, and practice questions is perfect for you.

If you are a “fluent” pro, this chapter will be a good review to make sure your skills are on point. Even if you are a pro, the ACT Science section often tests the basic skill of reading visuals in new and challenging ways, so this chapter will make sure you have strategies for both easy and hard questions.

Majority of the questions on the ACT Science section will just ask you to evaluate visuals and just relay information. To answer these questions, you need to read the graphs, tables, and/or scatterplots. Most of the passages in the ACT Science section just present you with a short paragraph or two as well as 1-4 visual representations of data (such as graphs, tables, and/or scatterplots). The passages will mention specific studies and label sections as Study 1/2/3.

The following are some of the important elements of a figure/table/chart:

### 1. Graph Axes

Axes are useful to figure out the control and the variable(s) in the experiment. Let’s take a look at this simple graph for practice:

In this graph, the x-axis measures the distance from the center of the plot to the nearest clearing. The y-axis measures the average change in AGTB (it is not important to understand what AGTB is).

The average change in AGTB would be considered the “dependent variable” in the research. For EXAMPLE: What is the average change in AGTB at a distance of 50 m from the center of the plot to the nearest clearing?

To do so, we first need to find 50 on the axis that defines the distance from the center to the nearest clearing, which is the x-axis. Next, we look on the y-axis for the value of the average change in AGTB and see that it reads 5 t/yr.

### 2. Units of Measure

The ACT Science section throws in these crazy weird units that you won’t have seen unless you studied high level Physics or Chemistry. **Don’t try to understand what the units mean** you do not need to know what they refer to in order to answer the questions.

For EXAMPLE in the previous figure, while you probably know that m is meters, you may be unfamiliar with the unit t/yr. Yet, you had no problem answering the question based on the above graph.

In all of the practice sections I’ve ever done, I have NEVER seen an ACT Science question ask you to convert the units from one form of measure to another. You most likely were taught this in Math and/or Science classes. Set those skills aside - you don’t need them here.

### 3. Independent and Dependent Variables

When looking at graphs and tables, you should keep in mind which variables are dependent and which are independent.

In general, an easy way to tell apart dependent and independent variable is to say the phrase “_____ depends on _____,” where the first blank is the dependent variable and the second is the independent variable.

For EXAMPLE, let’s say an experiment involves altering the amount of water given to plants and measuring their growth.

Look at both phrases and pick the one that makes sense: Amount of water depends on plant growth OR plant growth depends on amount of water

The second one makes sense - that how much the plants grow depends on how much water they get.

Let’s try another: Wind speed depended on the time of day OR The time of day depended on wind speed

Because wind speed is changing over time, the speed depends on the time, not the other way.

**Another easy tip is that independent variables are usually plotted on the x-axis, while dependent variables are plotted on the y-axis.** Using both the phrase and hints from graphs should allow you to distinguish independent from dependent variables.

With these goals in mind, let’s practice a question involving a graph and see how they can help us quickly understand and analyze the figure.

Reef coral is most at risk when temperatures consecutively exceed a 0.1 anomaly for several years. According to the above figure, the first such major period of trauma to coral was around** A.** 1900

**1945**

*B.***1990**

*C.***2000**

*D.*** Solution:** This graph depicts temperature anomalies from meteorological stations, showing both annual means and a five-year mean from 1880-2010. The graph is showing “the relationship between temperature anomalies and time”. Next, we can see that the variables are temperature anomalies (on the Y axis) and time (on the X axis).

We are looking for the first time period that the anomaly extends past .1 for several consecutive years i.e., when a few black dots in a row are all above the .1 line. As we

can see, this doesn’t really start until the late 1980s, as the last dip below .1 happened in about 1985. Thus, we can select answer option C, which is indeed several years of sustained anomalies.

### 4. Control Group

A control group is a trial in the experiment that is just being left alone. If you genetically change a tomato, you need a normal tomato first. If you plant different

types of enhanced fertilizer in fields, you need to benchmark with a normal fertilizer first.

Lets explain all the variables through the following example:

When looking at this figure, we can understand that pH is the variable being purposely changed and concentration (kg/L) is being measured.

Also, do you notice any other variables besides pH, exposure time, and concentration? How about water temperature? Or air pressure? No?

`If you are looking for additional variables because of a locator in a question and the locator directs you to a figure where you cannot find those variables, then you know they are constants. We can look at the figure to the left and deduce that anything besides pH, such as exposure time and concentration, is constant.

#### Example 2,3,4

So, when you look at a figure, find what is being changed, what is being measured, and then understand that everything else is constant.

2. Based on Samples 1-3, which element represents the independent variable?** A.** Sun

**Soil**

*B.***Water (mL)**

*C.***Height (cm)**

*D.*3. Based on Samples 1-3, which element represents the dependent variable?** A.** Sun

**Soil**

*B.***Water (mL)**

*C.***Height (cm)**

*D.*4. Based on Samples 1-3, which element(s) represent constants? (more than one answer may be correct)** A.** Sun

**Soil**

*B.***Water (mL)**

*C.***Height (cm)**

*D.*Solutions:

** 2.** In samples 1-3, notice that the amount of sun is changing, and the rest is constant. Another way to tell the difference is the Sun amount is being changed to pretty round numbers and the height is measured with ugly decimals. If you were to conduct and experiment, you would purposely change to pretty round numbers (independent variable) and you would measure ugly numbers (dependent variable). The correct answer is A.

** 3.** The height is changing, so thats the dependent variable. The correct answer is D.

** 4. **The sun and soil remain the same through samples 1-3, and those are the constants. The correct answer is A & B

## Types of Graphs

Since we have gone through the common elements of the graph, let’s check out the different types of graphs present in the Science passages.

### 1. Scatter Plot

Scatterplots are graphs of plotted points that show the relationship between two sets of data. For example, from the same passage as the earlier example:

In this example, each dot represents the measure of the average cumulative percent change in AGTB in a specific year. Let’s attempt this practice question: What was the average cumulative percent change in AGTB during Year 2?

To answer this question, we first need to find Year 2 on the x-axis. Follow that up to the Year 2 point on the scatterplot. Next, we look on the y-axis for the average cumulative percent change in AGTB and see that it reads 6%.

Scatterplots can be slightly more challenging if they ask you a question about a point not marked. These questions test your skills in interpolations and extrapolations.

### 2. Interpolations

The word itself seems complicated, but it simply means calculations of numbers between known data points (which are provided in the visuals). Let’s check out this ACT Science question:

#### Example 5

Based on the results of Study 1, if the distance from the center of a 100 m x 100 m plot were 75 m from the nearest clearing, the expected average change in the AGTB at the plot over 17 yr would be closest to which of the following** A. **- 1.1 t/yr

**- 2.6 t/yr**

*B.***+ 1.1 t/yr**

*C.***+ 2.6 t/yr**

*D.*** Solution**: You can simply draw a line connecting the dots in the scatterplot, and then, you approximate the point at 75 m from the center of the plot to the nearest clearing. See my diagram below:

Using this method, you can approximate the average change in AGTB at -2.8. This is closest to answer B, so that is the correct answer.

Now, some students may say that they cannot draw to save their life. However, you are not expected to paint like Picasso or paint the Sistine Chapel. Therefore, try to mark on the graph you are given and then use process of elimination.

This process gets a little trickier in extrapolations, in which we’ll calculate data that is beyond the bounds of what we’re given.

### 3. Extrapolations

In order to show how extrapolation works, we are going to work through an ACT Science practice question:

#### Example 6

Suppose that a sixth KI/H20 solution had been measured in Experiment 2 and the mass of the solution in the graduated cylinder was 67.54 g. The density of this solution would most likely have been closest to which of the following?** A.** 1.25 g/ml

**1.30 g/ml**

*B.***1.35 g/ml**

*C.***1.40 g/ml**

*D.*** Solution**: We’re figuring out the density that would match 67.54 g of solution in the graduated cylinder according to the table. The relationship between 60.63 g of solution and 64.64 g is +4.01 g of mass and +0.08 g/ml of density. The 67.54 g of solution (from the question) is above the highest 64.64g (Liquid 10) in the table. Figure out the exact mass difference between the two: 67.54 - 64.64 = 2.9

2.9 g is the mass difference as opposed to 4.01 g between the last and second to last entry. Between the second to last entry and last entry there was a +0.08 g/ml change in density. Since there is a slightly smaller mass change, the density change will be slightly smaller. So, the change should be about +0.06 g/ml. Add that to the last density value in the table: 1.29 + 0.06 = 1.35 g/ml. So, the answer is C. Even if you were slightly off, you would be correct.

#### Example 7

If, in Experiment 2, a \(15 \times 10^{-6}\) F capacitor had been used, the time required for the voltage across the capacitor to reach 6 V would have been closest to:

** A. **4.2 sec

**7.0 sec**

*B.***10.5 sec**

*C.***15.0 sec**

*D.*** Solution**: We need to use the table above. The highest given capacitance is \(1.2 \times 10^{-6}\) and we are asked about \(15 \times 10^{-6}\). The time for \(1.2 \times 10^{-6}\) was 8.3 seconds. The second highest given capacitance was \(0.6 \times 10^{-6}\) and the time for it was 4.2 seconds. The difference in time between 1.2 and 0.6 (the second highest given capacitance) is 8.3 - 4.2 seconds. So the difference is +4.1 seconds. The correct answer is A.

### 4. Ranking Lists

Sometimes the ACT will ask you to put data in increasing or decreasing order based on some criteria like height or mass.

#### Example 8

According to Tables 1 and 2, as the mass of successive sucrose samples increased, the change in the water temperature produced when the sample was burned most likely:** A.** increased only

**decreased only**

*B.***increased, then decreased**

*C.***decreased, then increased**

*D.*** Solution**: According to Table 1, the increasing order should be potato, egg, bread, cheese. Therefore, we can eliminate answer choices B and C because it ranks cheese before the other 3, which we know is wrong.

To decide between A and D, we need to look at Table 2. This is where mention of the heat released PER GRAM becomes very important. This entire table analyzes heat released by glucose, but the amount of grams changes.

The heat released by 1 g of sucrose is 16 kJ. Looking back at Table 1, see where 16 kJ fits in the heat released rankings. So, sucrose fits right in between. The final rankings should be Potato, egg, bread, sucrose, cheese. So, the answer is A.

### 5. Line Graphs

Line graphs are one of the harder types of visuals used in the science section. The reason is they show an infinite number of data points, and you need to be precise about the points you need. Also, this section often uses line graphs to show two different sets of data, one on the left and one on the right. See example graph:

To answer the example question “What is the RCRF in January 1990?”,

First you have to notice the correct line. The solid line represents RCRF according to the key. Match it up to the measurement on the right or left. The right side represents RCRF in %. It may help to create a straight line to find the point of intersection. See my example:

Then, find the point of intersection between that solid line and the January 1990 mark, which is around 7-7.5% so that is the answer.

So the key ACT Science strategies to remember with line graphs are:

- Identify the correct line
- Match it up to the correct measurement on the left or right
- Draw the point of intersection

### 7. Tricky Graphs

Let’s check out a graph that is not what it seems:

#### Example 9

Which of the following absorbed the most light across all wavelengths?*A.** *White S** B.** Orange S

**Red S**

*C.***Brown S**

*D.*** Solution**: First, let’s take a look at the graph. There are 5 lines here, and each one represents a different color of light plus Sulfur Oxide (which we do not need for this question, so we have to avoid it). Each graph represents the reflectance at each wavelength.

First, “absorb the most light” means the opposite of reflectance. Reflectance is what is graphed. The unprepared or rushed student would answer White S because they see it reflects the most light across all wavelengths, of the options in the answer choices. However, knowing that absorbance is the opposite of reflectance and looking across all wavelengths, I see that Brown S is reflecting the least. Therefore, it is absorbing the most, so the correct answer is D.

Rules to remember with graphs: **always compare what you are being asked to what the graph actually shows**. That way you don’t get tricked! Let’s check out another tricky graph:

#### Example 10

Which of the following would most likely NOT be found at a pressure of 10 kb?** A.** Facies A

**Facies C**

*B.***Facies G**

*C.***Facies E**

*D.*** Solution**: This graph is even more complex. There are 7 Facies identified (facies is a geology term for a body of rock with specified characteristics). The graph shows the pressure, depth, and temperature at which these 7 Facies appear.

The question is asking us for which of the following is NOT found at a pressure of 10 kb. Let’s break down this question.

First, pressure means we need to use the left y-axis. Second, we need to find 10 kb. Next, because the question asks what is likely NOT found at a pressure of 10kb, we need to draw a line across it.

Now, you can see that Facies C, G, and E all are around 10kb, but Facies A is not, so A is the correct answer.

The unprepared or rushed student might choose Facies C, G, or E as the answer if they missed the NOT, or that student might accidentally look at a depth of 10 km on the right instead of pressure and get the answer entirely wrong.

## Interpreting Trends

Interpreting trend questions can sometimes feel like looking into a crystal ball and predicting the future. Thankfully, no psychic powers are necessary to answer these questions.

Let me begin this section by emphasizing that you do not need to memorize any of the infinite number of possible trends to do well. In fact, simply knowing what the words “increasing” and “decreasing” mean should allow you to answer almost all of the questions regarding trends in data on the ACT. That being said, it’s useful to be familiar with a few common trends that you are likely to encounter.

### 1. Direct Correlations

While direct relationships are not always a line, it can be helpful to think of direct relationships as lines with a positive slope. As one increases, so does the other; as one

decreases so does the other. Here is a sample graph:

### 2. Inverse Correlation

As one increases, the other decreases. Shopping is a simple example, as you purchase more items, the amount of money you have decreases. Here is a sample graph of this inverse relationship:

### 3. Exponential Curve

Exponential trends are when one variable increases at an increasing rate. Visually, the value of that variable at first increases slowly, but then takes off, increasing faster and faster.

On a graph, this will look like a curved upward, or “J” shape, and in a table, you’ll see larger and larger increases in one variable for the same amount of increase in the other variable. Exponential trends can also be negative, although this is not as common. In a negative exponential graph, one variable will at first be decreasing slowly, but over time decrease faster and faster.Exponential trends are common when examining population or bacterial growth, which often see explosive increases after a slow start.

### 4. Logistic Curve

Data with logistic (or “S curve”) trends first increase slowly, then more sharply, before leveling off again. These trends are often seen in populations with limited resources - at first, the population can grow exponentially, but once resources runs out, the growth levels off.

### 5. No Trend

Remember, sometimes the data in a figure or table won’t follow any particular trend - don’t worry, this is often the case in real science, too! If you don’t see a trend between two variables, don’t panic. Instead, look for options that states “no trend” or “none of the above”.

As a general note when recognizing trends, you want to make sure you are looking at the big picture of what happens with the data. For instance, if a variable is increasing across the board except for one small exception, you can still conclude that the overall trend is increasing.