Data Representation
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ACT Science: Data Representation
Data Representation passages on the ACT Science section present scientific data in graphs, tables, and diagrams. These passages test your ability to read and interpret data—not to recall scientific facts. About 30-40% of ACT Science questions are Data Representation.
What You'll See
Data Representation passages typically include:
- Graphs (line graphs, bar graphs, scatter plots)
- Data tables
- Diagrams with measurements
- Brief text explaining the experiment or data collection
Key Insight: You do NOT need to know the science! These questions test your ability to read data carefully and draw conclusions from what's shown—not your background knowledge.
Reading Graphs: A Systematic Approach
Before answering any questions, examine:
- Title: What is being measured or compared?
- Axes: What variable is on each axis? What are the units?
- Scale: What are the intervals? Does it start at zero?
- Legend/Key: What do different lines, colors, or symbols represent?
- General trends: What overall patterns do you see?
Types of Graphs
| Graph Type | Best For | How to Read |
|---|---|---|
| Line Graph | Continuous data, trends over time | Follow the line; note increases, decreases, plateaus |
| Bar Graph | Comparing discrete categories | Compare heights of bars; read values from y-axis |
| Scatter Plot | Showing relationships between two variables | Look for patterns: positive correlation, negative correlation, no correlation |
| Pie Chart | Parts of a whole (percentages) | Compare slice sizes; look for labeled percentages |
Reading Data Tables
Table reading strategy:
- Read column headers to understand what's measured
- Identify independent variable (usually leftmost column)
- Identify dependent variables (other columns)
- Note units in headers or footnotes
- Look for patterns: Does value increase/decrease as another changes?
Common Question Types
| Question Type | What It Asks | Strategy |
|---|---|---|
| Find a value | "According to Figure 1, what was the temperature at time t = 5?" | Go directly to the graph/table; locate exact point |
| Identify trends | "As X increased, Y generally..." | Look at overall pattern, not individual points |
| Compare data | "Which trial had the highest value?" | Compare across rows/columns or different lines |
| Interpolation | "Based on the data, what would Y be when X = 25?" | Estimate between given data points |
| Extrapolation | "If the trend continues, what would Y be at X = 100?" | Extend the pattern beyond given data (less reliable) |
Recognizing Relationships
| Pattern | What It Looks Like | Description |
|---|---|---|
| Direct (positive) | Line goes up left to right | As X increases, Y increases |
| Inverse (negative) | Line goes down left to right | As X increases, Y decreases |
| No relationship | Scattered points, horizontal line | X and Y are not correlated |
| Linear | Straight line | Constant rate of change |
| Exponential | Curve that gets steeper | Rate of change increases |
| Logarithmic | Curve that flattens out | Rate of change decreases |
Common Pitfalls to Avoid
- Misreading axes: Double-check which variable is X and which is Y
- Ignoring units: A value of "5" could be 5 seconds, 5 minutes, or 5 hours
- Assuming causation: Correlation doesn't prove cause-and-effect
- Overlooking scale: A graph starting at 50 instead of 0 can exaggerate small changes
- Missing the legend: Different lines or symbols represent different conditions
đź’ˇ Examples
Practice interpreting data representations.
Example 1: Reading a Line Graph
Scenario: A graph shows "Plant Height (cm)" on the y-axis and "Days" on the x-axis. Three lines represent plants grown with different fertilizers (A, B, C). At Day 20, Fertilizer A shows 15 cm, B shows 22 cm, C shows 18 cm.
Question: Which fertilizer resulted in the tallest plants at Day 20?
Solution
Answer: Fertilizer B
At Day 20, compare the height (y-value) of each line: A = 15 cm, B = 22 cm, C = 18 cm. Fertilizer B produced the tallest plants.
Example 2: Identifying Trends
Scenario: A data table shows temperature increasing from 10°C to 50°C in 10° increments. For each temperature, the table shows reaction time decreasing: 45s, 32s, 20s, 12s, 8s.
Question: What is the relationship between temperature and reaction time?
Solution
Answer: Inverse relationship
As temperature increases (10→50°C), reaction time decreases (45→8s). This is an inverse (negative) relationship. Higher temperatures correlate with faster reactions.
Example 3: Interpolation
Scenario: A table shows drug concentration at different times: 0 hr = 100 mg/L, 2 hr = 75 mg/L, 4 hr = 50 mg/L, 6 hr = 25 mg/L.
Question: What would the concentration most likely be at 3 hours?
Solution
Answer: Approximately 62.5 mg/L
The concentration decreases by 25 mg/L every 2 hours (linear pattern). At 2 hr = 75, at 4 hr = 50. At 3 hours (halfway between), the concentration would be halfway between 75 and 50: (75+50)/2 = 62.5 mg/L.
Example 4: Comparing Multiple Variables
Scenario: A bar graph shows average test scores for three classes (A, B, C) across two years (2023, 2024). In 2023: A=75, B=80, C=70. In 2024: A=82, B=78, C=85.
Question: Which class showed the greatest improvement from 2023 to 2024?
Solution
Answer: Class C
Calculate improvement for each class:
- Class A: 82 - 75 = +7 points
- Class B: 78 - 80 = -2 points (actually decreased)
- Class C: 85 - 70 = +15 points
Class C improved by 15 points, the greatest increase.
Example 5: Reading Complex Data
Scenario: A scatter plot shows "Hours of Sleep" (x-axis, 4-10 hours) vs "Test Performance" (y-axis, 0-100%). Points cluster around a line that increases from lower-left to upper-right, but there's considerable scatter.
Question: Based on the data, which statement is best supported?
A) Getting more sleep guarantees higher test scores.
B) There is a positive correlation between sleep and test performance.
C) Sleep causes improved test performance.
D) Students who sleep 8 hours always score above 80%.
Solution
Answer: B
The upward trend shows a positive correlation—more sleep is associated with higher scores on average. However:
- A is wrong: "guarantees" is too strong; there's scatter in the data
- C is wrong: correlation doesn't prove causation
- D is wrong: "always" is too strong; the scatter means there are exceptions
B correctly describes the relationship without overstating.
✏️ Practice
Answer these data representation questions.
1. A line graph shows population growth. At year 0, population = 1000. At year 10, population = 2000. At year 20, population = 4000. What type of growth pattern is this?
A) Linear
B) Exponential
C) Inverse
D) No pattern
2. A table shows: Pressure (atm): 1, 2, 3, 4. Volume (L): 10, 5, 3.3, 2.5. What is the relationship between pressure and volume?
A) Direct
B) Inverse
C) No relationship
D) Exponential
3. A bar graph compares heights of plants grown in different light conditions. The y-axis goes from 50 cm to 60 cm. Plant A = 55 cm, Plant B = 58 cm. How much taller is Plant B than Plant A?
A) 3 cm
B) About 50%
C) 10 cm
D) Cannot be determined
4. Data shows enzyme activity at different pH values: pH 2 = 10%, pH 4 = 45%, pH 6 = 90%, pH 7 = 100%, pH 8 = 85%, pH 10 = 20%. At what pH is activity highest?
5. A scatter plot shows study time vs. grade with points clustered along a line going from lower-left to upper-right. A student who studied for 5 hours got a grade of 70%. According to the trend, a student who studied for 10 hours would most likely score:
A) Lower than 70%
B) About 70%
C) Higher than 70%
D) Exactly 100%
6. A graph shows temperature vs. time. The line is horizontal from t=0 to t=5, then rises steeply from t=5 to t=10. What happened at t=5?
7. Table data: Distance (m): 0, 10, 20, 30, 40. Time (s): 0, 2, 4, 6, 8. What is the speed of the object?
8. A graph shows two lines: Line A starts high and decreases; Line B starts low and increases. At what point would the two values be equal?
A) Where Line A starts
B) Where Line B starts
C) Where the lines cross
D) This can never happen
9. Data shows bacterial population doubling every 20 minutes. Starting population = 100. What would the population be after 1 hour?
10. A graph's y-axis is labeled "Concentration (mol/L)" and ranges from 0.0 to 0.5. A point appears to be at about 0.35. Which is the best estimate of the actual value?
A) 35
B) 0.35
C) 3.5
D) 350
Answer Key
- B) Exponential — Population doubles each period (1000→2000→4000), which is exponential, not linear (constant addition).
- B) Inverse — As pressure increases, volume decreases. This is inverse proportionality (Boyle's Law).
- A) 3 cm — 58 - 55 = 3 cm. The truncated y-axis (50-60) might make the difference look larger visually, but the actual difference is just 3 cm.
- pH 7 — Activity is 100% at pH 7, the highest value in the data.
- C) Higher than 70% — The positive correlation (upward trend) suggests more study time associates with higher grades.
- The system began heating — Temperature was constant (possibly a phase change or heating not applied), then began to rise at t=5.
- 5 m/s — Speed = distance/time. The object travels 10 m every 2 s, so speed = 10/2 = 5 m/s (or 40/8 = 5 m/s).
- C) Where the lines cross — The intersection point is where both values are equal.
- 800 — In 1 hour (60 min), there are 3 doubling periods (60/20 = 3). Population: 100 → 200 → 400 → 800.
- B) 0.35 — The units are mol/L, and the scale goes 0.0 to 0.5, so 0.35 mol/L is correct. Always pay attention to units!
âś… Check Your Understanding
1. Why is it important to check whether a graph's y-axis starts at zero?
Show Answer
When a graph's y-axis doesn't start at zero, small differences can appear exaggerated. For example, if bars representing values of 95 and 100 are shown on an axis from 90-100, the difference looks dramatic (100 appears twice as tall as 95), when it's actually only a 5% difference. Always calculate actual differences rather than judging visually.
2. What is the difference between interpolation and extrapolation?
Show Answer
Interpolation estimates values between known data points (within the range of the data). Extrapolation estimates values beyond the known data points (outside the data range). Interpolation is generally more reliable because you're staying within observed patterns. Extrapolation is riskier because trends might not continue beyond the measured range.
3. A graph shows a strong correlation between ice cream sales and drowning deaths. Does this prove ice cream causes drowning?
Show Answer
No! This is a classic example of correlation not proving causation. Both ice cream sales and drowning deaths increase in summer due to a confounding variable: hot weather. More people buy ice cream when it's hot; more people swim (and unfortunately, some drown) when it's hot. The variables are correlated but one doesn't cause the other.
4. What's the first thing you should do when you see a new graph or table on the ACT?
Show Answer
Read the labels! Before trying to interpret data, identify: (1) What variables are shown (titles, axis labels); (2) What units are used; (3) What the scale is; (4) What different lines/colors/symbols represent (legend). Many errors come from misreading what the data actually shows. This takes only a few seconds but prevents careless mistakes.
🚀 Next Steps
- Review any concepts that felt challenging
- Move on to the next lesson when ready
- Return to practice problems periodically for review