Comparing Data Sets - ACT Science

SECTION 1

Historical Context & Motivation

The ability to compare data sets is one of the most fundamental skills in science, and it has a long history stretching back centuries. Before formal statistical methods existed, scientists relied on careful observation and side-by-side comparison of recorded measurements to draw conclusions about the natural world. From early astronomers comparing planetary observations across different nights to physicians comparing patient outcomes across treatments, comparing data sets has always been the backbone of scientific reasoning.

On the ACT Science test, roughly 40% of questions fall under the Interpretation of Data category, and a significant portion of those require you to look at two or more tables, graphs, or figures and identify patterns, differences, or relationships between them. Understanding the history of how scientists have compared data gives you insight into why these questions are structured the way they are.

1600s • Early Scientific Tables

Scientists like Galileo and Kepler began organizing astronomical observations into structured tables, enabling side-by-side comparison of planetary data across different time periods.

1786 • Birth of Statistical Graphics

William Playfair invented the bar chart and line graph, giving scientists powerful visual tools for comparing data sets at a glance rather than poring over raw numbers.

1900s • Rise of Controlled Experiments

Ronald Fisher formalized experimental design, introducing the concept of control groups and treatment groups—two data sets designed specifically to be compared.

1959 • ACT Test Introduced

The American College Testing program launched, eventually incorporating a Science section that heavily tests students' ability to interpret and compare data presented in multiple formats.

The central question that data comparison addresses is straightforward yet powerful: How does one variable or condition affect outcomes differently than another? Whether you are comparing growth rates of two plant species under different light conditions, or examining how temperature changes affect two different chemical reactions, the skill of reading across data sets is something you will use not only on the ACT but throughout your academic and professional life.

SECTION 2

Core Principles of Comparing Data Sets

Before diving into specific ACT question types, you need to understand the foundational principles that govern how scientists—and test-makers—think about data comparison. These principles will help you approach any passage with confidence, whether the data appears in tables, graphs, or a mixture of both.

Identify Common Variables

To compare data sets meaningfully, they must share at least one common variable—typically the independent variable (the thing being changed). If two graphs share the same x-axis, they are designed to be compared.

Check Scales and Units

Always verify that two data sets use the same scales and units before drawing conclusions. A graph in milligrams and another in grams could mislead you if you don't convert first.

Look for Trends, Not Just Points

A single data point can be an outlier. Compare the overall trends—increasing, decreasing, constant, or cyclical patterns—across both data sets to identify real differences.

Note Where Data Sets Intersect or Diverge

Pay special attention to intersection points (where two lines or values are equal) and divergence points (where they begin to separate). These are common question targets.

Connect Data to Experimental Context

Always relate what you see in the data back to the passage's experimental setup. Understanding why two groups differ (different treatments, conditions, or materials) helps you explain what the data means.

SECTION 3

Visual Explanation — Reading Two Data Sets at Once

The diagram below simulates a common ACT Science scenario: two experiments measured the growth of two different plant species over the same time period. Study how the two data lines share the same axes, which makes direct comparison straightforward. Notice where the lines cross, how their slopes differ, and what happens at the endpoints.

This graph shows two plant species measured over 6 weeks. Species A (cyan) grows at a steeper rate than Species B (pink). Note the intersection at Week 2, where both species have the same height, and the growing divergence after that point.

When you encounter a graph like this on the ACT, your first step should be to read the title and axis labels carefully. The x-axis shows the shared independent variable (time in weeks), and the y-axis shows the dependent variable (height in cm). Because both species are plotted on the same axes, you can directly compare their values at any given week. For instance, at Week 4, Species A is at about 15 cm while Species B is at about 9 cm—a difference of roughly 6 cm. The intersection point at Week 2 is especially important because it tells you that before Week 2, Species B was actually taller, but after Week 2, Species A surpasses it and continues to pull ahead.

SECTION 4

How to Compare — Strategies and Techniques

While the ACT Science section does not require you to perform complex calculations, you will often need to identify quantitative relationships between data sets. Understanding a few key concepts will help you handle these questions quickly and accurately.

Recognizing Trends

The most common comparison question asks whether two data sets show the same or different trends. A direct relationship means both variables increase together (or both decrease together). An inverse relationship means one increases while the other decreases. On the ACT, you might see one data set with a direct relationship and another with an inverse relationship—and a question will ask you to compare them.

RATE OF CHANGE

Rate = (y₂ − y₁) ÷ (x₂ − x₁)

Where y₂ and y₁ are two data values from the dependent variable, and x₂ and x₁ are two corresponding values from the independent variable. A larger rate indicates a steeper trend.

You can use rate of change to quantify how quickly data is increasing or decreasing. When comparing two data sets, computing the rate of change for each allows you to say with confidence that one is changing faster than the other. For example, if Species A grows at a rate of approximately 4.0 cm per week and Species B grows at about 1.7 cm per week, you can conclude that Species A grows more than twice as fast.

Comparing Magnitudes

PERCENT DIFFERENCE

% Difference = |Value A − Value B| ÷ ((Value A + Value B) ÷ 2) × 100

This formula helps you express how different two values are in relative terms. A small percent difference means the data sets are similar, while a large percent difference indicates a significant gap.

Comparing Across Different Formats

Sometimes the ACT presents one data set in a table and another in a graph, or two tables with slightly different column structures. In these cases, you need to translate between formats mentally. The key strategy is to find the common variable shared between the two presentations and use it as your bridge. Read specific values from the graph and compare them to the corresponding row in the table, or vice versa.

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ACT TIP

SECTION 5

Comparing Data Across Tables and Graphs

On the ACT, data comparison questions often involve multiple tables or a combination of tables and graphs. The diagram below illustrates a common scenario: two experiments measuring the solubility of two different salts in water at various temperatures. Study how the table and graph present the same type of information in different ways.

This diagram demonstrates how the ACT might present two data sets in different formats. Salt A appears in a table and shows a small, gradual increase in solubility. Salt B appears in a graph and shows a steep, dramatic increase. The shared variable—temperature—lets you compare them directly.

The key insight here is that even though the data is presented in two different formats, the underlying comparison is the same. Salt A has a relatively flat trend—its solubility barely changes with temperature (an increase of only 9 g/100mL over 70°C). Salt B, on the other hand, shows a steep upward trend (an increase of 87 g/100mL over the same temperature range). A typical ACT question might ask: "At which temperature does Salt B first exceed Salt A in solubility?" or "Which salt's solubility is more affected by temperature?" By translating the graph into approximate numbers and comparing to the table, you can answer these confidently.

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WATCH OUT

SECTION 6

Worked Example — Comparing Growth Data

Let's walk through a complete ACT-style question using the plant growth data from Section 3. The question reads: "Based on the data, at what week does Species A first exceed Species B in height, and by approximately how much does Species A exceed Species B at Week 6?"

Worked example

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Step 1 — Read the Question Carefully

The question has two parts: (1) identify the week when Species A first exceeds Species B, and (2) calculate the approximate difference at Week 6. This tells us we need to look for the intersection point and then read values at the endpoints.
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Step 2 — Locate the Intersection

Looking at the graph, the two lines cross at approximately Week 2. Before Week 2, Species B is slightly taller. After Week 2, Species A is taller. Therefore, Species A first exceeds Species B during Week 3 (the first whole-week data point after the intersection).

Species A first exceeds Species B after the Week 2 intersection point.
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Step 3 — Read Values at Week 6

From the graph at Week 6: Species A is at approximately 24 cm and Species B is at approximately 11 cm. To find the difference, we subtract: 24 − 11 = 13 cm.

At Week 6, Species A exceeds Species B by approximately 13 cm.
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Step 4 — Verify Reasonableness

This answer makes sense because Species A has a steeper slope (faster growth rate), so the gap between the two species should widen over time. At Week 3, the difference was small (about 10 − 8 = 2 cm), and by Week 6 it has grown to 13 cm. The divergence is consistent with the different growth rates.
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Step 5 — Select the Answer

On a multiple-choice ACT question, you would look for an answer choice that states Species A first exceeds Species B around Week 2–3 and that the difference at Week 6 is approximately 13 cm. If exact values aren't offered, choose the closest option.

Final Answer: Species A exceeds Species B starting around Week 2–3; the difference at Week 6 is ≈ 13 cm.

SECTION 7

Strengths and Limitations of Different Comparison Methods

Different types of data presentations have their own strengths and weaknesses when it comes to making comparisons. Understanding these will help you quickly determine the best approach for any ACT Science question.

Comparison Method	Strengths	Limitations
Side-by-side graphs	Trends are immediately visible; intersection and divergence points easy to spot; good for comparing rates of change.	Exact values can be hard to read; different y-axis scales can mislead; colors may be hard to distinguish.
Two separate tables	Precise values are easy to read; good for exact comparisons at specific data points; no visual distortion.	Trends are harder to see; requires more mental effort to picture the overall pattern; slower to process.
Overlaid lines on one graph	Best format for direct comparison; differences are visually obvious; shared axes guarantee same scale.	Can become cluttered with more than 3–4 data sets; overlapping lines near intersection points are hard to read.
Bar charts (grouped)	Excellent for comparing discrete categories; easy to see which category is largest/smallest at each point.	Poor at showing continuous trends; the eye may compare bar heights inaccurately for similar values.
Mixed format (table + graph)	Tests multiple reading skills; one format may clarify what the other obscures.	Requires translating between formats; easy to misread values if you rush; often the hardest question type.

Common data comparison formats on the ACT Science section

SECTION 8

Connecting to Advanced ACT Question Types

Basic data comparison skills form the foundation for the more advanced question types you will encounter on the ACT Science section. As you become more comfortable with straightforward comparisons, you should be prepared for questions that layer in additional complexity. Understanding how comparing data sets connects to other ACT Science skills will help you see the bigger picture.

Basic Comparison Skill	Advanced ACT Application
Reading values from two data sets at the same x-value	Interpolation and extrapolation: predicting values between or beyond measured data points across multiple experiments
Identifying whether trends are direct or inverse	Evaluating hypotheses: determining whether a scientist's hypothesis is supported by comparing predicted trends to actual data across two studies
Finding intersection points between two data sets	Conflicting Viewpoints passages: identifying where two scientists' claims agree or disagree based on overlapping data
Comparing rates of change (slopes)	Research Summaries passages: explaining why one experimental method produced faster results than another
Translating between tables and graphs	Multi-passage synthesis: using data from one experiment to answer questions about a different but related experiment

How basic comparison skills build toward advanced ACT question types

As you continue preparing for the ACT, keep in mind that approximately 15–18 of the 40 Science questions require some form of data comparison. The Research Summaries passage format (which makes up about half of the test) is specifically designed to present multiple experiments with related but different data sets, making comparison skills essential. Students who can quickly and accurately compare data across figures consistently score in the upper ranges of the Science section.

SECTION 9

Practice Problems

Use the following practice problems to test your ability to compare data sets. The problems increase in difficulty, mimicking the range you might encounter on the actual ACT Science section. Refer back to the diagrams and tables from earlier sections as needed.

Question 1: CONCEPTUAL

Two data sets are plotted on the same graph with the same x-axis (time) and y-axis (temperature). Data Set 1 shows a steady increase, while Data Set 2 remains constant. Which of the following best describes the relationship between the two data sets over time?A) The two data sets increase at the same rate, maintaining a constant difference throughout. B) The two data sets converge over time, becoming closer in value as time increases. C) The difference between the two data sets increases over time, as Data Set 1 rises while Data Set 2 stays the same. D) The two data sets are identical at all points in time.

Show answer

Data Set 1 increases steadily while Data Set 2 remains constant. At any given time, the gap between them equals Data Set 1's value minus Data Set 2's fixed value — a difference that grows larger as time increases. The two data sets diverge over time. Answer: C

Question 2: BASIC CALCULATION

The table below shows the height (in cm) of two plant species measured every two weeks over a 6-week period.Based on the data in the table, what are the approximate rates of growth (in cm/week) for Species A and Species B, respectively, over the 6-week period?

A. Species A: approximately 1.5 cm/week; Species B: approximately 3.8 cm/week
B. Species A: approximately 3.8 cm/week; Species B: approximately 1.5 cm/week
C. Species A: approximately 4.8 cm/week; Species B: approximately 2.2 cm/week
D. Species A: approximately 3.8 cm/week; Species B: approximately 3.8 cm/week

Show answer

To find the average rate of growth over the 6-week period, use the formula: Rate = (final height − initial height) ÷ (total weeks). For Species A: Rate = (24 − 1) ÷ (6 − 0) = 23 ÷ 6 ≈ 3.8 cm/week. For Species B: Rate = (11 − 2) ÷ (6 − 0) = 9 ÷ 6 = 1.5 cm/week. So Species A grows at approximately 3.8 cm/week and Species B at approximately 1.5 cm/week, making answer choice B correct. Why the other choices are wrong: • Choice A reverses the two rates, assigning Species A's rate to Species B and vice versa — a common error when reading table columns in the wrong order. • Choice C results from using incorrect starting values (e.g., using 0 instead of the Week 0 heights of 1 and 2), giving (24 − 0) ÷ 5 ≈ 4.8 and (11 − 0) ÷ 5 ≈ 2.2 — an error from dividing by 5 weeks instead of 6 and ignoring initial heights. • Choice D incorrectly assigns the same rate (3.8 cm/week) to both species, ignoring that Species B's total change (9 cm) is different from Species A's (23 cm).

Question 3: INTERMEDIATE

A researcher measured the solubility of two salts at various temperatures. Salt A's solubility was recorded in the table below, and Salt B's solubility was recorded in the graph below.Table 1: Solubility of Salt AFigure 1: Solubility of Salt B (g/100 mL) vs. Temperature (°C) The graph shows the following approximate data points for Salt B: 20°C → 10 g/100 mL 40°C → 26 g/100 mL 60°C → 55 g/100 mL 80°C → 96 g/100 mL 100°C → 140 g/100 mLBetween 40°C and 80°C, which salt's solubility changes more, and by approximately how much more does it change compared to the other salt?

A. Salt A's solubility changes more, by approximately 67 g/100 mL more than Salt B.
B. Salt B's solubility changes more, by approximately 67 g/100 mL more than Salt A.
C. Salt B's solubility changes more, by approximately 70 g/100 mL more than Salt A.
D. Both salts show the same change in solubility between 40°C and 80°C.

Show answer

Step 1: Find Salt A's change in solubility from 40°C to 80°C using the table. Salt A at 40°C = 37 g/100 mL; Salt A at 80°C = 40 g/100 mL. Change for Salt A = 40 − 37 = 3 g/100 mL. Step 2: Find Salt B's change in solubility from 40°C to 80°C using the graph. Salt B at 40°C ≈ 26 g/100 mL; Salt B at 80°C ≈ 96 g/100 mL. Change for Salt B = 96 − 26 = 70 g/100 mL. Step 3: Compare the two changes. Salt B changes by 70 g/100 mL and Salt A changes by only 3 g/100 mL. Difference = 70 − 3 = 67 g/100 mL. Salt B's solubility changes more, by approximately 67 g/100 mL more than Salt A. The correct answer is B.

Question 4: APPLIED

A researcher is designing an experiment to purify a compound using recrystallization. She needs a salt whose solubility changes dramatically with temperature so that she can dissolve a large amount at high temperature and then crystallize most of it out at low temperature. Use the solubility data in the table below to answer the question.Which salt should the researcher choose, and what temperature range would make the recrystallization process most effective?

A. Salt A; cooling from 80°C to 10°C, because its solubility increases steadily and allows the most crystals to form.
B. Salt B; cooling from 80°C to 10°C, because its solubility drops from 96 g/100 mL to 9 g/100 mL, allowing approximately 87 g to crystallize out per 100 mL of water.
C. Salt A; cooling from 60°C to 20°C, because its solubility changes by the greatest amount in that range.
D. Salt B; cooling from 40°C to 20°C, because the solubility difference is largest in that temperature range for Salt B.

Show answer

Step 1 — Determine the solubility range for each salt between 10°C and 80°C: • Salt A: 31 g/100 mL at 10°C → 40 g/100 mL at 80°C. Difference = 40 − 31 = 9 g/100 mL. • Salt B: 9 g/100 mL at 10°C → 96 g/100 mL at 80°C. Difference = 96 − 9 = 87 g/100 mL. Step 2 — Identify which salt has the more dramatic solubility change: Salt B changes by 87 g/100 mL versus only 9 g/100 mL for Salt A, so Salt B is far superior for recrystallization. Step 3 — Identify the most effective temperature range: Dissolving at 80°C (maximum solubility of 96 g/100 mL) and cooling to 10°C (minimum solubility of 9 g/100 mL) maximizes the amount that crystallizes out (~87 g per 100 mL). Step 4 — Eliminate incorrect choices: • Choice A is wrong because Salt A's solubility changes only 9 g/100 mL total — poor for recrystallization. • Choice C is wrong for the same reason (Salt A) and the stated range (60°C to 20°C) is not optimal. • Choice D is wrong because the 40°C to 20°C range for Salt B yields only a 25 − 11 = 14 g/100 mL difference, far less than the 87 g achievable from 80°C to 10°C. The correct answer is B.

Question 5: CRITICAL THINKING

A plant growth study tracks three species over several weeks. Species A starts at a height of 1 cm and grows at approximately 3.8 cm/week. Species B starts at a height of 2 cm and grows at approximately 1.5 cm/week. Species C starts at 0 cm and grows at a constant rate of 3.0 cm/week. Without graphing, at approximately what week would Species C overtake Species B, and would Species C ever overtake Species A?

A. Species C overtakes Species B at approximately week 1.3 and overtakes Species A at approximately week 4.5.
B. Species C overtakes Species B at approximately week 2.0 and overtakes Species A at approximately week 3.0.
C. Species C overtakes Species B at approximately week 1.3 but never overtakes Species A because Species A grows faster than Species C.
D. Species C never overtakes Species B or Species A because it starts at 0 cm, giving it too large a deficit to overcome.

Show answer

Species C height: 3.0w. Species B height: 2 + 1.5w. Setting equal: 3.0w = 2 + 1.5w → 1.5w = 2 → w ≈ 1.3 weeks. For Species A: 3.0w = 1 + 3.8w → -0.8w = 1 → w = -1.25, which is negative and meaningless, so Species C never overtakes Species A. Correct answer: C.