Grade: Grade 11 Subject: Science Unit: ACT Science Reasoning SAT: ProblemSolving+DataAnalysis ACT: Science

Data and Graphs

Learn

This lesson teaches you to interpret scientific data presented in tables, graphs, and figures. Data interpretation is the most common question type on the ACT Science section, appearing in virtually every passage.

Types of Data Displays

  • Line Graphs: Show trends and relationships between continuous variables over time or across conditions
  • Bar Graphs: Compare discrete categories or groups
  • Scatter Plots: Display relationships between two variables, useful for identifying correlations
  • Tables: Present precise numerical data in organized rows and columns
  • Pie Charts: Show proportions of a whole (less common on ACT)

Reading Graphs Effectively

  1. Read the title: Understand what the graph is measuring
  2. Check axis labels: Identify what each axis represents and its units
  3. Note the scale: Check if axes start at zero and whether intervals are consistent
  4. Identify trends: Look for patterns (increasing, decreasing, constant, cyclical)
  5. Locate specific values: Use gridlines to find exact data points when needed

Common Graph Relationships

  • Direct/Positive Relationship: As X increases, Y increases
  • Inverse/Negative Relationship: As X increases, Y decreases
  • No Relationship: Variables show no consistent pattern
  • Exponential: Rapid increase or decrease (curved line)
  • Linear: Constant rate of change (straight line)

ACT-Specific Strategies

  • Many questions ask you to read values directly from graphs - practice precision
  • Interpolation: Estimating values between data points
  • Extrapolation: Predicting values beyond the range of data (use trend lines)
  • Compare multiple data sets on the same graph carefully

Examples

Example 1: Reading Table Data

A table shows bacterial colony counts at different temperatures:

Temperature (C)Colony Count (thousands)
2012
2528
3045
3552
4038

Question: At what temperature was bacterial growth greatest?

Solution: Look for the highest value in the Colony Count column. 52 thousand colonies occurred at 35C, so bacterial growth was greatest at 35C.

Example 2: Identifying Trends

A line graph shows dissolved oxygen levels in a lake from June to September. The line starts at 9 mg/L in June, decreases to 6 mg/L in August, then rises to 7.5 mg/L in September.

Question: Describe the trend in dissolved oxygen over the summer.

Solution: Dissolved oxygen decreased from June through August, reaching its lowest point in August, then partially recovered in September. This likely correlates with temperature changes and algae activity.

Example 3: Interpolation

Data points show: at 100g, a spring stretches 2cm; at 200g, it stretches 4cm.

Question: How much would the spring stretch with 150g?

Solution: The relationship is linear (each 100g adds 2cm). At 150g (halfway between 100g and 200g), the stretch would be 3cm (halfway between 2cm and 4cm).

Example 4: Comparing Multiple Data Sets

A graph shows growth curves for three species of bacteria: Species A peaks at 30C, Species B peaks at 45C, Species C peaks at 60C.

Question: Which species would dominate in a hot spring at 55C?

Solution: At 55C, Species C (which peaks at 60C) would be near its optimal temperature, while Species A and B would be well past their peaks. Species C would dominate.

Practice

Complete these practice problems to strengthen your data interpretation skills.

1. A graph shows population growth of rabbits over 10 years. Year 1: 50, Year 3: 150, Year 5: 450, Year 7: 1350, Year 9: 4050. What type of growth pattern does this represent? Estimate the population at Year 6.

2. A table shows enzyme activity at different pH levels: pH 4 (20 units), pH 5 (45 units), pH 6 (80 units), pH 7 (95 units), pH 8 (75 units), pH 9 (30 units). At what pH is enzyme activity optimal? Describe the overall relationship between pH and activity.

3. Two lines on a graph show heart rate over time. Line A shows a steady 70 bpm. Line B starts at 70 bpm, rises to 140 bpm at minute 5, then returns to 70 bpm by minute 10. Which line represents a person who exercised? What happened at minute 5?

4. A scatter plot shows the relationship between study hours and test scores. Points form a loose upward pattern from (1, 60) to (6, 90) with some variation. What type of correlation exists? Can you conclude that more study time causes higher scores?

5. Data shows water pressure at different ocean depths: 0m (1 atm), 10m (2 atm), 20m (3 atm), 30m (4 atm). Predict the pressure at 50m depth. What mathematical relationship exists between depth and pressure?

6. A bar graph compares average rainfall in four cities. City A: 120cm, City B: 45cm, City C: 90cm, City D: 60cm. Rank the cities from driest to wettest. City C receives how many times more rainfall than City B?

7. A graph shows radioactive decay. Starting amount: 100g. After 1 half-life: 50g. After 2 half-lives: 25g. After 3 half-lives: 12.5g. If one half-life equals 5 years, how much material remains after 20 years?

8. Two experiments are shown on the same graph. Experiment 1 shows a steep positive slope. Experiment 2 shows a gradual positive slope. Both start at the origin. At x = 10, which experiment has a higher y-value? What does the slope difference indicate?

9. A table shows plant height over 6 weeks: Week 1 (2cm), Week 2 (4cm), Week 3 (8cm), Week 4 (14cm), Week 5 (18cm), Week 6 (20cm). Between which two weeks did the plant grow fastest? When did growth begin to slow?

10. A graph shows temperature change over time when ice is heated. The line rises from -10C to 0C, stays flat at 0C for a period, then rises again from 0C to 100C, stays flat at 100C, then rises above 100C. Explain what is happening during the flat portions of the graph.

Check Your Understanding

Test your comprehension with these review questions.

1. What should you always check first when examining a graph?

Show Answer

Check the title, axis labels, and units. Understanding what is being measured and how it is measured is essential before interpreting any data.

2. What is the difference between interpolation and extrapolation?

Show Answer

Interpolation estimates values between known data points. Extrapolation predicts values beyond the range of available data. Extrapolation is less reliable because the trend may not continue.

3. If a graph shows an inverse relationship, what happens to Y as X increases?

Show Answer

In an inverse (negative) relationship, as X increases, Y decreases. The graph would show a downward-sloping line or curve.

Next Steps

  • Practice reading graphs quickly - speed is essential on the ACT
  • Create flashcards for graph vocabulary (trend, correlation, interpolation, etc.)
  • Move on to the next lesson: CER Writing