Reasoning from data

Read the graph directly. Find 70 °F on the x-axis (air temperature), move up to the data point, then across to the y-axis (chirps in 15 seconds). The point sits on the gridline for 30 chirps.

Step by step:

1. The x-axis shows temperature and the y-axis shows chirps, so start on the x-axis at 70.
2. Go up to the line: the point is at the height of the 30 gridline.
3. Check the neighbors: 65 °F gives 25 chirps and 75 °F gives 35, so 30 at 70 °F fits the pattern.
4. Choice D (70) repeats the temperature, which is the x-value, not the answer.

The correct answer is C, 30 chirps.

Tip: Always say the axes aloud ("temperature across, chirps up") before reading a value. It stops you from reporting the wrong axis.

62 °F was not measured, so we interpolate: estimate a value between two measured points.

Step by step:

1. The nearest measured points are 60 °F → 20 chirps and 65 °F → 25 chirps.
2. Between them, the line rises 5 chirps over 5 °F, which is 1 chirp per °F.
3. 62 °F is 2 °F above 60 °F, so add 2 chirps: 20 + 2 = 22 chirps.
4. Check: 22 is between 20 and 25, and closer to 20, just as 62 is closer to 60 than to 65.

The correct answer is A, about 22 chirps.

Tip: Interpolation means estimating inside the range of the data. The answer must fall between the two neighboring values. Any choice outside that range (like 25 or 62) is wrong.

Describe both the direction and the shape of the data.

Step by step:

1. Direction: as temperature rises from 55 °F to 80 °F, chirps rise from 15 to 40. The trend is upward (eliminates B).
2. Shape: each 5 °F step adds exactly 5 chirps (15 → 20 → 25 → 30 → 35 → 40). Equal steps make a straight line, a steady (linear) increase. It does not level off (eliminates C).
3. Choice D adds a cause-and-effect claim the graph cannot show. The data are about air temperature, and nothing in the study made crickets chirp on purpose.

The correct answer is A.

Tip: Equal changes in y for equal changes in x = a straight line (linear). Changes that grow larger = curving up; changes that shrink = leveling off.

Read the value directly from the graph. The x-axis is time heated (minutes) and the y-axis is water temperature (°C). Find 4 minutes on the x-axis and move straight up to the data point. From there, move across to the y-axis: the point sits a little above the 50 °C gridline, at 52 °C.

Step by step:

1. Name the axes: time across, temperature up.
2. Locate 4 on the time axis.
3. Go up to the point and across: 52 °C.

The correct answer is 52 °C.

Check: The temperature rises 16 °C every 2 minutes. Starting at 20 °C, after 2 minutes it is 36 °C and after 4 minutes it is 36 + 16 = 52 °C. That matches.

Tip: Before reading any graph value, say the two axes out loud. It keeps you from reading the wrong point or the wrong axis.

This is interpolation: estimating a value between two measured points. The graph shows 52 °C at 4 minutes and 68 °C at 6 minutes. Because the points lie on a straight line, the temperature at 5 minutes should be halfway between them.

Step by step:

1. Find the readings on each side of 5 minutes: 52 °C (4 min) and 68 °C (6 min).
2. Find the halfway value: \dfrac{52 + 68}{2} = 60 °C.
3. On the graph, the line crosses the 5-minute gridline exactly at the 60 °C gridline.

The correct answer is 60 °C.

Check: The water warms 8 °C per minute. From 20 °C, after 5 minutes: 20 + 5 \times 8 = 60 °C. Same answer.

Tip: For a value between two data points, use the points on both sides. Picking just the nearest point gives a value that is too high or too low.

Read the table carefully, one row at a time. In the column Trained storm spotters, the value 41 appears in the row for Delling County. Move across that row to the last column, Tornadoes reported, 2015–2024: the value is 27.

Step by step:

1. Find the right column: trained storm spotters.
2. Find 41 in that column (Delling).
3. Stay in the Delling row and read the tornado column: 27.

The correct answer is 27 tornadoes.

Check: Delling's population density is 160 — a different column. Corwin (22 spotters) reported 19 tornadoes, and Easton (75 spotters) reported 34. Only Delling has 41 spotters.

Tip: Use a finger or a straight line on your erasable note board to stay on one row. Most table-reading errors come from sliding to the row above or below.

Test each description against the numbers in the table: "| 0 | 100 |", "| 1 | 200 |" … "| 4 | 1,600 |".

Step by step:

1. Increases each hour: +100, +200, +400, +800. The increase gets bigger every hour, so the population is not growing by the same amount (eliminates A and D).
2. Ratios each hour: ×2, ×2, ×2, ×2. The population doubles every hour (B).
3. Choice C says growth slowed down, but the increases are getting larger, not smaller.
4. D comes from taking the first increase (100) and assuming it repeats, which the later hours contradict (200 → 400 is an increase of 200).

The correct answer is B.

Tip: When a quantity doubles over equal time periods, it grows faster and faster. On a graph it curves upward more and more steeply.

The passage's final sentence is the key: "The flask holds a fixed amount of broth, and no new nutrients are added during the experiment."

Step by step:

1. The data cover only 0–4 hours, a period when there was plenty of food and space.
2. Predicting 48 hours ahead is extrapolation far beyond the data.
3. As the bacteria multiply, they use up the fixed supply of nutrients and produce wastes. Growth must slow and eventually stop. Real cultures level off (and may decline) instead of doubling forever.
4. Choice A contradicts the table, which shows growth in every hour. Choice C is false: the experiment kept the flask at 37 °C, and nothing says the temperature changed. Choice D reverses the data, since the population grew.

The correct answer is B.

Tip: Be cautious about predictions far outside the data range. Ask what conditions might change, such as limited food, space or time.

Read the overall pattern. For eleven of the twelve months, points with more ice cream cones sold also have more sunburn cases: from (5, 2) at the lower left to (28, 30) at the upper right. That is a positive correlation.

Step by step:

1. The data show the two variables tend to rise and fall together (choice C).
2. A correlation alone does not prove cause and effect, so choice A goes too far. The newspaper's headline asks exactly that question, but the data cannot answer it.
3. Choice B describes a negative correlation, the opposite of the plot.
4. Choice D says "every month," but one month (22 thousand cones, 3 sunburn cases) does not follow the pattern, so the claim about every month is too absolute.

The correct answer is C.

Tip: Data like these can show that two variables are related, but only a controlled experiment can show that one causes the other. Prefer choices with careful words like "tended to."

When two variables rise and fall together but neither causes the other, a third variable may be causing both. The plot has one point per month, which hints at seasons.

Step by step:

1. Hot, sunny months make people want cold treats, so ice cream sales go up.
2. The same hot, sunny months mean more time outdoors in strong sunlight, so sunburns go up.
3. So sunny, warm weather (choice D) explains both trends.
4. Choice A (price of ice cream) might affect sales but has no link to sunburn. Choice B (number of clinics) might affect how many people are treated but not ice cream sales. Choice C (flavors) affects neither sunburn nor the seasonal pattern.

The correct answer is D.

Tip: For any correlation, ask: "Is there a hidden factor that could drive both?" Weather, age, population size and time are common hidden factors.

Compare the two rows of the table. Enzyme A has its highest activity, 90 units, at pH 2. Enzyme B has its highest activity, 95 units, at pH 8.

Step by step:

1. Enzyme A peak: pH 2 (90). Enzyme B peak: pH 8 (95).
2. pH 2 is lower than pH 8, so Enzyme A is most active at a lower pH.
3. Test the others: at pH 7, A = 0 and B = 85, so A is not more active. At pH 9, B still has 70 units, so B has not stopped. At pH 5, A = 10 and B = 35, so neither is at its peak.

The correct answer is Enzyme A is most active at a lower pH than Enzyme B.

Check: The passage says A works in the acidic stomach and B in the slightly basic intestine — consistent with A's peak at a lower pH.

Tip: When a table has two rows, put your finger on the correct row before reading. Many wrong answers come from reading the other enzyme's number.

This is extrapolation: extending a trend beyond the measured data. The highest station (3,000 m) averages −2 °C. The pattern drops 6 °C per 1,000 m, which is 3 °C per 500 m.

Step by step:

1. Extra elevation: 3{,}500 - 3{,}000 = 500 m.
2. Expected drop for 500 m: \dfrac{6}{2} = 3 °C.
3. Expected temperature: -2 - 3 = -5 °C.

The correct answer is −5 °C.

Check: Use the whole pattern: start at 16 °C at sea level and subtract 6 °C per 1,000 m. 16 - 3.5 \times 6 = 16 - 21 = -5 °C. Both methods agree.

Tip: When you extend a trend, keep the same direction and the same rate. Going higher keeps getting colder; it does not level off or reverse unless the data or passage say so.

The question asks about the change between seasons, so compute a difference for each habitat.

Evidence from the graph (spring − winter):

• Forest: 34 - 20 = 14
• Wetland: 42 - 15 = 27
• Grassland: 18 - 12 = 6
• Suburban: 22 - 19 = 3

Step by step:

1. List the four differences: 14, 27, 6, 3.
2. The smallest difference is 3, for the suburban habitat.

The correct answer is Suburban.

Check: Grassland has the shortest bars, but the question is about change, not size. Its change (6) is twice the suburban change (3).

Tip: In grouped bar graphs, decide first whether the question wants a value (one bar), a total, or a difference (gap between paired bars).

Repeated trials at the same temperature should give similar results. Compare each value with the other trials in its row and with the overall trend.

Step by step:

1. In most rows the three trials are within about 2 beats of each other (for example, 199, 201, 200 at 20 °C).
2. At 25 °C, Trials 1 and 3 are 239 and 241, but Trial 2 is 180 — about 60 beats lower.
3. The trend rises about 40 beats per 5 °C (160 → 200 → 240 → 280), so about 240 is expected at 25 °C. The value 180 does not fit.

The correct answer is 25 °C, Trial 2 (180 beats/min).

Check: 281 at 30 °C is the largest number in the table, but it fits both its row (279, 280) and the trend, so it is not an outlier.

Tip: An outlier is judged against its neighbors, not by being the biggest or smallest number. In a repeated-trials table, scan each row first.

Use only the two lines on the graph. Phosphorus: 20, 24, 29, 35, 41, 33, 26, 22 µg/L. Bloom days: 8, 12, 18, 25, 34, 30, 21, 15.

Step by step:

1. Both lines rise from Year 1 to Year 5, peak in Year 5, and fall through Year 8. Years with more phosphorus had more bloom days, so choice B is supported.
2. Choice A claims phosphorus caused the blooms. Phosphorus does feed algae (the passage says so), but a graph of two lines moving together cannot by itself prove that cause, so "graph alone" makes A too strong.
3. Choice C is false: bloom days fell after Year 5.
4. Choice D extrapolates to Year 10 and to zero. The decline is already slowing (drops of 8, 7, then 4 µg/L), so the graph does not support it.

The correct answer is B.

Tip: "Best supported by the data" usually means the most careful statement. A choice that describes the pattern beats a choice that claims a cause or predicts far into the future.

The classmate extended the straight line beyond the data: 8 °C per minute for 4 more minutes gives 100 + 4 \times 8 = 132 °C. The math is correct, but the science makes the trend stop. The passage says the experiment was at sea level, "where pure water boils at 100 °C," and that "The water began to boil at the 10-minute reading."

Step by step:

1. A trend can only be extended while the conditions that produced it stay the same.
2. Once water boils, added heat energy changes liquid water into steam (a change of state). The temperature of the boiling water stays at about 100 °C.
3. So the line should flatten at 100 °C, not keep climbing to 132 °C.

The correct answer is the water stays at about 100 °C while it boils, because the energy goes into turning liquid water into steam.

Check: Liquid water at sea level is never at 132 °C in an open pot; steam escapes and the pot keeps boiling at 100 °C.

Tip: Before extending any trend, ask: "Is there a limit — a boiling point, a full battery, a 100% maximum, a food supply — that will stop this pattern?"

Combine the table with the text. The passage says the stomach is "about pH 2" and the small intestine is "about pH 8." The table shows Enzyme A (stomach) peaks at pH 2 with 90 units, and Enzyme B (intestine) peaks at pH 8 with 95 units.

Step by step:

1. Enzyme A's best pH (2) matches the stomach's pH (2).
2. Enzyme B's best pH (8) matches the small intestine's pH (8).
3. So each enzyme works best at about the pH of the organ where it is found.
4. Eliminate overreaching or unsupported choices: activity does not always rise with pH (A falls after pH 2); "importance" was never measured; B at pH 2 has 0 activity.

The correct answer is each enzyme is most active at about the pH of the organ where it is found.

Check: Both data points needed for the conclusion are in the passage — nothing outside the data is assumed.

Tip: A supported conclusion uses only what the data show. Watch for words like always, more important, or predictions about conditions that contradict the table.

You need both sources. Graph: rainfall went from 20 mm in July to 30 mm in August — an increase. Table: creek depth went from 35 cm in July to 30 cm in August — a decrease. Text: "Beginning in early August, farms upstream started pumping water out of the creek."

Step by step:

1. More rain would normally raise the creek, yet the creek dropped.
2. Something else must be removing water. The passage names one: pumping for irrigation.
3. So the August data are consistent with pumping lowering the creek.

The correct answer is rainfall increased from July to August, but creek depth still decreased, which is consistent with water being pumped out upstream.

Check: July (20 mm), not August, had the least rain. The data cannot show exactly how many centimeters the pumping removed, because rain and pumping were acting at the same time.

Tip: In two-source questions, write down what each source says for the same time period before choosing. The right answer must agree with both.

The friend extended the pattern: 20 + 1.2 \times 120 = 164%. The arithmetic is correct, but the passage defines the battery level as "a percent of a completely full battery (100%)." A battery cannot hold more than a full charge.

Step by step:

1. The steady pattern only describes the first 40 minutes.
2. At 1.2 points per minute, the battery would reach 100% after \dfrac{80}{1.2} \approx 67 minutes.
3. After that the level cannot keep rising; it stays at 100% (most phones also charge more slowly as they get close to full).

The correct answer is the level cannot go above 100%, so the straight-line pattern must stop once the battery is full.

Check: Any prediction above 100% contradicts the passage's own definition of the measurement.

Tip: Extrapolation is risky when it runs into a natural limit — 100% full, a boiling point, a food supply, or space in a container. Ask whether the answer is even possible.

The pattern is a correlation: as population density and spotters increase (15 → 300 people per square mile; 4 → 75 spotters), reported tornadoes increase (6 → 34). But the passage gives two key facts:

• "…the five counties had about the same number of strong thunderstorms."
• "A tornado is added to the official record only if someone sees it or its damage and reports it."

Step by step:

1. If storms were about equal, the real number of tornadoes was probably similar in each county.
2. In places with few people, more tornadoes go unseen and unreported.
3. So more people and spotters lead to more reports, not more tornadoes.

The correct answer is more people and spotters mean more tornadoes are seen and reported, even though the counties probably had a similar number of tornadoes.

Check: This explanation agrees with every fact in the passage; each other choice contradicts the radar records or the rules for reporting.

Tip: Always ask how data were collected. When data depend on someone noticing an event, more observers can create a pattern that is not really there.

Read the bloom-day values from the red line (right axis): Year 5 = 34 days, Year 8 = 15 days.

Step by step:

1. Change: 34 - 15 = 19 days fewer.
2. Divide by the original (starting) value, Year 5: \text{percent decrease} = \frac{34 - 15}{34} \times 100 = \frac{19}{34} \times 100 \approx 55.9\%
3. Round: about 56%.
4. Traps: 19% treats the number of days as a percent. 44% is \tfrac{15}{34}, the part that remains, not the part that was lost. 127% divides by the new value (15) instead of the original.

The correct answer is A, about 56%.

Check: 34 \times 0.56 \approx 19, and 34 - 19 = 15 ✓

Tip: In percent change, always divide by the value you started from. A percent decrease can never be more than 100%.

A correlation (two things changing together) does not prove that one causes the other, because a third factor might be involved. The table has a third column: distance to the nearest highway. It rises from 0.3 km in Ash Park to 4.8 km in Fairview — the same rows where tree cover rises and asthma visits fall. The passage also states that traffic exhaust "can trigger asthma attacks."

Step by step:

1. Neighborhoods with the most trees are also the farthest from a highway.
2. Living farther from heavy traffic could reduce asthma attacks by itself.
3. So distance from traffic is a possible confounding variable; the data cannot show how much of the difference, if any, comes from the trees.

The correct answer is neighborhoods with more trees are also farther from a major highway, so residents may breathe less traffic exhaust.

Check: The other choices either use data the table does not contain, predict the opposite pattern, or describe the method rather than a cause.

Tip: When a question asks what else could explain a pattern, look for a variable that changes along with both of the others.

Percent decrease compares the change with the starting value.

Evidence from the graph: Wetland spring = 42 species; wetland winter = 15 species.

Step by step:

1. Change: 42 - 15 = 27 species.
2. Starting value (spring): 42.
3. Percent decrease: \dfrac{27}{42} \times 100 \approx 64.3\%, so about 64%.

The correct answer is about 64%.

Check: 64% of 42 is about 27, and 42 - 27 = 15, the winter count. ✔

Tip: Always divide by the value you started from. Dividing by the ending value (27 ÷ 15 = 180%) or reporting the remaining part (15 ÷ 42 ≈ 36%) are the two most common percent-change mistakes.

This combines interpolation with handling an outlier.

Evidence from the table: At 25 °C the trials that agree are 239 and 241 (Trial 2, 180, is the unusual result). At 30 °C the trials are 281, 279 and 280.

Step by step:

1. Typical value at 25 °C: \dfrac{239 + 241}{2} = 240 beats/min.
2. Typical value at 30 °C: \dfrac{281 + 279 + 280}{3} = 280 beats/min.
3. Halfway: \dfrac{240 + 280}{2} = 260 beats/min.

The correct answer is about 260 beats per minute.

Check: The trend rises about 8 beats per °C (for example, 200 at 20 °C to 280 at 30 °C). From 240 at 25 °C, 2.5 °C more adds 2.5 \times 8 = 20: 260. ✔

Tip: If you average in an outlier, every value you calculate from it is off. Here, the mean at 25 °C with the outlier is (239 + 180 + 241) \div 3 \approx 220, which would give a wrong estimate of about 250.