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Reasoning from Scientific Data

Learn to describe trends, estimate values inside and beyond the data, tell correlation from causation, and draw conclusions the data truly support.

Practice this skill 22 min Reasoning from data Leer en español
Key idea

What you'll learn

Once you can read a table or graph, the next step is to reason with it: to see patterns, make predictions, and decide what the data mean. That is what scientists do every day, and it is a major part of the GED Science test.

In this lesson you will learn to:

  • describe trends (increasing, decreasing, leveling off, peaking, cycling);
  • interpolate (estimate between data points) and extrapolate (predict beyond the data), and know when extrapolation is risky;
  • tell linear patterns (add the same amount) from exponential patterns (multiply by the same amount);
  • distinguish correlation from causation and spot third variables and outliers;
  • calculate rate of change and percent change;
  • pick the conclusion that is best supported by the data.

How it shows up on the GED: Questions like "Which conclusion is best supported by the data?", "Based on the trend, predict…", "Which statement describes the relationship?" and "What is the percent decrease?" appear throughout the Science test, often attached to graphs with two data series or to a graph plus a table.

Words to know

Key terms

  • data — measurements or observations (numbers of chirps, temperatures).
  • trend — the general direction of the data over time or across a variable (steadily rising).
  • interpolate — estimate a value between measured data points (chirps at 62 °F when 60 °F and 65 °F were measured).
  • extrapolate — predict a value beyond the measured range (bacteria after 48 hours when only 0–4 hours were measured).
  • linear relationship — y changes by the same amount for each equal step in x; graphs as a straight line (+5 chirps per 5 °F).
  • exponential growth — a quantity multiplies by the same factor in each equal time period (bacteria doubling every hour).
  • leveling off (plateau) — the changes get smaller until the values stay about the same.
  • correlation — two variables change together; positive = both rise together, negative = one rises as the other falls.
  • causation — one variable actually produces a change in another.
  • third (confounding) variable — a hidden factor that affects both correlated variables (sunny weather affects ice cream sales and sunburns).
  • outlier — a data point far from the overall pattern.
  • rate of change — how much y changes per unit of x (chirps per °F).
  • percent change — the change as a percent of the original value.
  • conclusion — a statement about what the data show; a supported conclusion stays within the evidence.

All Science words in the glossary

1. Describing trends

Describe a trend with two pieces: direction and shape.

PatternWhat the numbers doGraph looks like
steady increasegoes up by the same amount each stepstraight line rising
steady decreasegoes down by the same amount each stepstraight line falling
increasing, then leveling offgoes up by smaller and smaller amountsrising curve that flattens
speeding upgoes up by larger and larger amountscurve that gets steeper
peakrises, reaches a maximum, then fallshill shape
cyclerepeats up and downwaves (seasons, tides)
no trendno consistent changescattered points
Seven small graphs showing trend shapes: steady increase is a straight rising line; steady decrease is a straight falling line; increasing then leveling off is a rising curve that flattens; speeding up is a curve that gets steeper; peak is a hill shape; cycle is a repeating wave; no trend is scattered points. Describe a trend by direction AND shape steady increase steady decrease rises, then levels off speeding up peak (hill) cycle (waves) no trend

Example: Crickets chirped 15, 20, 25, 30, 35, 40 times at 55, 60, 65, 70, 75, 80 °F. Each 5 °F adds 5 chirps → steady increase (linear).

Example: Coffee cooled 90 → 70 → 57 → 48 → 42 °C every 5 minutes. Drops of 20, 13, 9, 6 → decreasing, leveling off.

2. Interpolation and extrapolation

Interpolation is estimating a value inside the range of your data. It is usually reliable, especially when the pattern is smooth.

Example: Chirps at 60 °F = 20, at 65 °F = 25. At 62 °F: the rate is 1 chirp per °F, so 20 + 2 = 22 chirps. The answer must be between 20 and 25.

Extrapolation is predicting outside the range. It is useful for short steps but becomes risky the farther you go, because conditions can change.

Example: Bacteria doubled every hour from 0 to 4 hours (100 → 1,600). Predicting 5 hours (3,200) is a small, reasonable step. Predicting 48 hours (about 28,000 trillion) is not, because a flask has limited food. Growth will slow and stop. On the GED, an answer that extrapolates far beyond the data is usually a trap, unless the question tells you to assume the pattern continues.

Limits in nature: Plants stop responding to more fertilizer, populations hit a carrying capacity, and a cooling object stops cooling at room temperature. Ask what would limit the trend.

3. Linear vs. exponential patterns

Check a table two ways:

  • Differences (subtract each value from the next). Equal differences → linear.
  • Ratios (divide each value by the one before). Equal ratios → exponential.
Hour01234
Linear example100200300400500
Exponential example1002004008001,600
Graph comparing a linear and an exponential pattern over 0 to 4 hours. Linear: 100, 200, 300, 400, 500, adding 100 each hour, a straight line. Exponential: 100, 200, 400, 800, 1,600, doubling each hour, a curve that gets steeper. Both take the same first step from 100 to 200, so check more than one step. Linear (add the same) vs. exponential (multiply the same) 0 400 800 1,200 1,600 0 1 2 3 4 Hour Amount 400 800 500 1,600 linear: +100 each hour exponential: ×2 each hour same first step

Both start with the same first step (+100), so look at more than one step before deciding. The exponential example grows faster and faster. Exponential growth appears in bacteria and other populations with unlimited resources, and exponential decay appears in radioactive half-life (the amount halves each half-life).

4. Correlation is not causation

A correlation means two variables change together. On a scatter plot:

  • positive correlation: points rise from lower left to upper right;
  • negative correlation: points fall from upper left to lower right;
  • no correlation: no clear pattern.
Three scatter plots. Positive correlation: points rise from lower left to upper right. Negative correlation: points fall from upper left to lower right. No correlation: points show no clear pattern. Reading a scatter plot: what kind of correlation? Positive correlation Negative correlation None (no correlation) A correlation shows variables change together, not that one causes the other.

Correlation alone does not prove causation. Three possibilities exist when A and B are correlated:

  1. A causes B.
  2. B causes A (reversed causation).
  3. A third variable C causes both. (Ice cream sales and sunburns both rise in sunny summer months.) It could also be coincidence, especially with small data sets.

How do scientists show causation? With a controlled experiment: change only A, keep everything else the same, and see whether B changes. Observational data (surveys, monitoring) can suggest causes but cannot prove them alone.

Outliers: A point far from the pattern (22 thousand cones but only 3 sunburns) should be investigated. It may be a measurement error or a real, unusual event.

5. Drawing supported conclusions

The GED loves the phrase "best supported by the data." The best-supported conclusion:

  • matches the actual numbers (direction, peak, comparison);
  • stays within the data: same organisms, same conditions, same time range;
  • uses careful language ("tended to", "in this study", "on average");
  • does not claim cause from correlation alone.

Red flags in answer choices: always, never, every, all, only, proves, will definitely, predictions far outside the data, and claims about variables that were never measured.

When there are two sources (a graph and a table), line them up by the shared variable, such as year, and check each claim against both.

Formula

Rate of change and percent change

Rate of change (how fast y changes per unit of x):

\text{rate of change} = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}

Example: chirps go from 20 at 60 °F to 40 at 80 °F: \dfrac{40 - 20}{80 - 60} = \dfrac{20}{20} = 1 chirp per °F.

Percent change:

\text{percent change} = \frac{\text{new} - \text{original}}{\text{original}} \times 100

A negative result is a percent decrease. Example: bloom days 34 → 15: \dfrac{15 - 34}{34} \times 100 \approx -56\%, a 56% decrease.

A Science question may not give you these formulas, so learn them; they are standard arithmetic. You may use the on-screen calculator.

Worked example

Worked example 1: Interpolating from a table

Stimulus:

Air temperature (°C)0102030
Speed of sound (m/s)331337343349

Question: Estimate the speed of sound at 25 °C. A. 343 m/s B. 346 m/s C. 349 m/s D. 355 m/s

Think-aloud:

  1. 25 °C is between 20 °C (343) and 30 °C (349), so this is interpolation.
  2. Each 10 °C adds 6 m/s, so 5 °C adds 3 m/s.
  3. 343 + 3 = 346 m/s.
  4. A and C are the neighboring values; D is outside the range.
Line graph of the speed of sound versus air temperature: 331 meters per second at 0 degrees Celsius, 337 at 10, 343 at 20 and 349 at 30. The value at 25 degrees is interpolated halfway between 343 and 349: each 10 degrees adds 6 meters per second, so 5 degrees adds 3, giving 346 meters per second. Interpolating: estimate between two measured points 328 332 336 340 344 348 352 0 5 10 15 20 25 30 Air temperature (°C) Speed of sound (m/s) 331 337 343 349 25 °C → 346 m/s +6 m/s per 10 °C → +3 m/s per 5 °C answer must lie between 343 and 349

Answer: B, 346 m/s.

Worked example

Worked example 2: The limits of extrapolation

Stimulus: A 20 cm candle burns down 2 cm every hour. A student measures it at 0, 1, 2 and 3 hours: 20, 18, 16, 14 cm.

Question: Which prediction is reasonable? A. After 6 hours, the candle will be 8 cm tall. B. After 12 hours, the candle will be −4 cm tall. C. After 3 hours, the candle will start growing. D. The candle will burn faster and faster.

Think-aloud:

  1. Pattern: −2 cm per hour (linear decrease).
  2. 6 hours: 20 - 2 \times 6 = 8 cm. A short, reasonable extrapolation. ✓
  3. 12 hours: the formula gives 20 - 24 = -4 cm, which is impossible. The candle is gone after 10 hours. The trend has a physical limit.
  4. C and D contradict the steady pattern.
Graph of candle height versus time. Measured points: 20 centimeters at 0 hours, 18 at 1, 16 at 2 and 14 at 3, a drop of 2 centimeters per hour. A dashed extension shows a reasonable short extrapolation to 8 centimeters at 6 hours, continuing to 0 centimeters at 10 hours when the candle is gone. A dotted red extension below zero reaches minus 4 centimeters at 12 hours, which is impossible: the trend has a physical limit. Extrapolating: short steps OK, watch for limits −6 −4 −2 0 2 4 6 8 10 12 14 16 18 20 22 0 2 4 6 8 10 12 Time (hours) Candle height (cm) impossible zone measured (−2 cm/h) 6 h: 8 cm ✔ reasonable 10 h: 0 cm, gone 12 h: −4 cm ✘

Answer: A.

Worked example

Worked example 3: Correlation or causation?

Stimulus: "A study of 50 cities found that cities with more public libraries also had more traffic accidents."

Question: Which is the best explanation for this correlation? A. Libraries cause traffic accidents. B. Traffic accidents cause cities to build libraries. C. Larger cities have more people, which leads to both more libraries and more accidents. D. The correlation proves libraries should be closed.

Think-aloud:

  1. Is there a hidden factor that affects both? Yes: population size.
  2. More people → more libraries are needed AND more cars on the road → more accidents.
  3. A and B claim direct causes with no evidence; D draws a policy conclusion from a correlation.
Diagram of a third variable. Population size, the hidden factor, points with arrows to more public libraries and to more traffic accidents. A dashed line between libraries and accidents is labeled correlated, but not cause and effect. Larger cities have more of both. Correlation explained by a third variable Population size (hidden third variable) More public libraries More traffic accidents more people need more libraries more people, more cars correlated but libraries do NOT cause accidents

Answer: C. The third variable (population) explains the correlation.

Worked example

Worked example 4: Percent change

Stimulus: A biologist counted 250 trout in a stream in 2020 and 200 trout in 2024.

Question: What was the percent change in the trout population? A. −50% B. −25% C. −20% D. +20%

Think-aloud:

  1. Change: 200 - 250 = -50 trout.
  2. Divide by the original value (2020): \dfrac{-50}{250} = -0.20.
  3. Multiply by 100: −20%, a 20% decrease.
  4. A treats 50 trout as 50%. B divides by the new value (50 \div 200 = 25\%). D has the wrong sign.
Bar chart of trout counts: 250 in 2020 and 200 in 2024. The change is 200 minus 250, which is minus 50 trout. Divide by the original value, 250: minus 50 divided by 250 equals minus 0.20, which is a 20 percent decrease. Percent change: divide by the ORIGINAL value 0 50 100 150 200 250 300 Trout counted 250 2020 (original) 200 2024 (new) −50 change = 200 − 250 = −50 −50 ÷ 250 = −0.20 × 100 = −20% (a 20% decrease)

Answer: C, −20%.

Common mistake

Common mistakes to avoid

  • Treating correlation as causation. Wrong: "Ice cream causes sunburn." Right: "They are correlated; warm sunny weather likely drives both."
  • Extrapolating too far. Wrong: "The bacteria will keep doubling for two days." Right: "Limited nutrients will slow growth; the pattern holds only for the range measured."
  • Assuming linear growth. Wrong: 100, 200, 400, 800 → next is 1,000 (adding 200). Right: check ratios: ×2 each time → 1,600.
  • Interpolating outside the bracket. Wrong: estimating 25 chirps at 62 °F. Right: the estimate must lie between the values at 60 °F (20) and 65 °F (25), so 22.
  • Wrong base for percent change. Wrong: dividing by the new value. Right: always divide by the original value.
  • Overgeneralizing. Wrong: "This proves the ban was the only cause." Right: "Phosphorus fell after the ban; other factors cannot be ruled out from these data."
Test strategy

GED test strategy

  • Read the question stem first. Is it asking for a trend, an estimate, a cause or a calculation?
  • Describe the trend in your own words before looking at the choices: "rises steadily", "peaks in Year 5".
  • For estimates, find the two nearest data points and make sure your answer lies between them (interpolation), or extend the pattern only one or two steps (extrapolation).
  • Check differences AND ratios in tables to identify linear vs. exponential patterns.
  • Choose cautious wording. "Tended to", "is associated with" and "in this study" beat "proves", "always" and "causes" when the data come from observation.
  • With two sources, match them by the shared variable and test each claim against both.
  • Calculator: use it for percent change, but estimate first so you can spot a wrong keystroke (19 ÷ 34 is a bit more than half).
Calculator tip

Calculator tip (TI-30XS MultiView)

For percent change from 34 to 15: type ( 1 5 − 3 4 ) ÷ 3 4 × 1 0 0 then enter. The display shows about −55.88, a decrease of about 56%. Use the subtraction key − between numbers and the negative key (−) only to enter a negative number. Always put the subtraction in parentheses so it is done before dividing.

Check yourself

Reasoning from data
Crickets as Thermometers

Crickets are cold-blooded, so their bodies warm and cool with the air around them. A naturalist counted how many times field crickets chirped in 15 seconds on evenings with different air temperatures. The graph shows the average number of chirps at each temperature.

Line graph titled Cricket chirps and air temperature. The x-axis is air temperature in degrees Fahrenheit from 50 to 85, with gridlines every 5 degrees. The y-axis is average number of chirps in 15 seconds from 0 to 45, with gridlines every 5 chirps. Data points: 55 °F 15 chirps; 60 °F 20; 65 °F 25; 70 °F 30; 75 °F 35; 80 °F 40. The points lie on a straight rising line. 50 55 60 65 70 75 80 85 0 5 10 15 20 25 30 35 40 45 Air temperature (°F) Chirps in 15 seconds

According to the graph, about how many times do crickets chirp in 15 seconds when the air temperature is 70 °F?

Answer choices
Hint

Find 70 on the x-axis, go straight up to the line, then straight across to the y-axis.

Check yourself

Reasoning from data
Crickets as Thermometers

Crickets are cold-blooded, so their bodies warm and cool with the air around them. A naturalist counted how many times field crickets chirped in 15 seconds on evenings with different air temperatures. The graph shows the average number of chirps at each temperature.

Line graph titled Cricket chirps and air temperature. The x-axis is air temperature in degrees Fahrenheit from 50 to 85, with gridlines every 5 degrees. The y-axis is average number of chirps in 15 seconds from 0 to 45, with gridlines every 5 chirps. Data points: 55 °F 15 chirps; 60 °F 20; 65 °F 25; 70 °F 30; 75 °F 35; 80 °F 40. The points lie on a straight rising line. 50 55 60 65 70 75 80 85 0 5 10 15 20 25 30 35 40 45 Air temperature (°F) Chirps in 15 seconds

Based on the graph, about how many chirps in 15 seconds would you expect at an air temperature of 62 °F?

Answer choices
Hint

62 °F lies between two measured temperatures. Where between them does it fall?

Summary

  • Describe a trend by its direction and its shape (steady, speeding up, leveling off, peaking).
  • Interpolated values must fall between neighboring data points; extrapolate only a short distance, and watch for natural limits.
  • Equal differences mean linear; equal ratios mean exponential.
  • Correlation does not prove causation; look for third variables and investigate outliers.
  • Percent change = (new − original) ÷ original × 100; choose conclusions that stay within the data and use careful language.
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