GRE · Data Analysis · TOPIC LESSON
Read a display’s variables, scale and reference group before calculating from a shared data set.
BY THE END, YOU CAN
BEFORE YOU START
Original educational lesson. Work through the examples before revealing the practice answers. This original lesson supports current GRE General Test study; it does not reproduce official questions, certify a writing score or predict test content.
LEARN THROUGH ORIGINAL PRACTICE
All teaching passages, writing prompts, examples and exercises in this lesson are original. No official ETS questions, prompts or explanations are reproduced. Current structure and observed public sample metadata are separate from this original teaching; no official score or question probability is implied.
01 / UNDERSTAND & APPLY
Start with the title, population, time period, axis labels, units, legend and any footnotes. Determine whether entries are counts, percentages, rates, cumulative totals or values in thousands. A value of 2.4 on an axis labeled “thousands of dollars” means $2400, not $2.40.
Data Interpretation is a shared-data context or question set, not an additional exclusive response type. Questions using the same table or graph still require a single choice, multiple choices or numeric entry as directed. Each question may use a different denominator, and an answer to one should not silently become a premise for another.
03 / UNDERSTAND & APPLY
A bar graph compares category magnitudes using a labeled numerical axis. A grouped bar graph distinguishes subcategories through a legend; a stacked bar’s total height is a total and its segment lengths are parts. Read segment boundaries carefully when the segment does not start at zero.
A line graph plots successive values, often over time. A steep rise indicates change relative to the horizontal scale, not necessarily the largest final value. A connecting segment does not prove exact values between observed dates unless interpolation or a continuous model is specified. Truncated axes can exaggerate visual differences; use labels, not apparent bar ratios.
Full-size scientific diagram. Swipe or scroll horizontally; keyboard users can focus the diagram and use arrow keys.
ORIGINAL WORKED EXAMPLE
Using the bookstall data, what is the percentage increase in total sales from February to March?
Answer 300/7%, approximately 42.9%
04 / UNDERSTAND & APPLY
An overall proportion equals the sum of relevant counts divided by the sum of all counts. It is not generally the unweighted average of separate row percentages. Rows with more observations deserve more weight.
In the bookstall data, January and February have equal totals of 70 but March has 100. A monthly proportion from March therefore contributes more to the three-month proportion. Keep exact totals as long as possible rather than averaging rounded percentages.
ORIGINAL WORKED EXAMPLE
What fraction of all bookstall books sold over the three months were nonfiction?
Answer 3/8
05 / UNDERSTAND & APPLY
In a circle graph, sector fraction=central angle/360°. To convert a share to a count, multiply by the stated total. The same percentage on two different charts need not mean the same amount if the totals differ. Check that displayed categories form a complete nonoverlapping whole before adding their shares.
The original budget chart allocates 50% to materials, 30% to staffing and 20% to transport. The angles are 180°,108° and 72°. A 20% sector means one fifth of the total, not a fixed currency amount.
Full-size scientific diagram. Swipe or scroll horizontally; keyboard users can focus the diagram and use arrow keys.
ORIGINAL WORKED EXAMPLE
The displayed budget totals $1800. How much more is allocated to materials than transport?
Answer $540
06 / UNDERSTAND & APPLY
A frequency table gives counts for values or bins. A histogram uses adjacent intervals on a numerical axis rather than unrelated categories. Identify which bin includes a boundary value. Here the first three bins include the left endpoint and exclude the right; the last includes both.
For equal-width frequency bins, height gives the count. If widths differ, read the graph’s stated vertical measure: a density histogram uses area, not raw height, for frequency or proportion. Grouped data generally do not reveal exact within-bin values, so a mean estimated from midpoints is an approximation.
Full-size scientific diagram. Swipe or scroll horizontally; keyboard users can focus the diagram and use arrow keys.
ORIGINAL WORKED EXAMPLE
The displayed waiting-time histogram has counts 2,5,3,2 in bins [0,10),[10,20),[20,30),[30,40] minutes. What fraction waited at least 20 minutes?
Answer 5/12
07 / UNDERSTAND & APPLY
A basic boxplot marks minimum, first quartile, median, third quartile and maximum. The displayed summary 2,5,9,14,20 has IQR 9 and range 18. The numerical width from Q₁ to median need not equal the width from median to Q₃, even though both span comparable portions of the ordered positions.
Do not derive an exact mean, mode or individual data count from a five-number summary alone. If whiskers exclude separately plotted outliers, they are not the minimum and maximum of the full data set; use the stated convention.
Full-size scientific diagram. Swipe or scroll horizontally; keyboard users can focus the diagram and use arrow keys.
08 / UNDERSTAND & APPLY
A scatterplot places two measured variables on separate axes; each point records one pair. An upward tendency suggests positive association, a downward tendency negative association, and no clear pattern may indicate weak association. Outliers can influence the apparent pattern.
The displayed original study-hour and quiz-point pairs are (1,2),(2,3),(3,3),(4,5),(5,4),(6,7). The tendency is broadly positive but not perfectly increasing. Observational association does not establish that extra study caused a particular score: other factors, selection and measurement can matter. A fitted trend or interpolation is not an exact prediction for each person.
09 / UNDERSTAND & APPLY
Labeled table entries can support exact arithmetic. A point read between coarse gridlines may support only an estimate, unless exact coordinates are supplied. Do not invent precision from the width of a drawn mark. Verify whether the question requests a ratio, percent, percentage points, difference or rate.
For multiple-answer data questions, test every statement against the same source data and select the complete correct set. For numeric entry, use the requested units and rounding instruction. Re-read a shared data set for each question rather than carrying a denominator from the previous one.
10 / UNDERSTAND & APPLY
All examples and practice in this lesson are original. For quantitative comparison (QC), use A if Quantity A is greater, B if Quantity B is greater, C if they are equal, and D if the relationship cannot be determined from the information given. A, B or C must hold for every permitted case. To establish D, give two allowed cases producing different relationships; an inability to calculate is not itself evidence for D.
A single-answer question requires one choice. For multiple-answer questions, obey the stated selection count or select every correct option if instructed. Test each option separately; do not stop after finding one. Multiple-answer questions receive credit only when the complete correct set is selected, with no incorrect choices. Numeric entry requires the requested value, with units handled in the calculation; round only when the question directs you to. A single numeric-entry box accepts an integer or decimal; a pair of fraction boxes accepts an integer numerator and a nonzero integer denominator. Fractions need not be reduced, but reducing makes checks easier. Do not enter a percent sign when the requested number is a percentage. Preserve exact fractions until the last step.
A calculator can check arithmetic but cannot decide the domain, interpretation or denominator for you. Estimate sign and size first, enter parentheses carefully, and compare the result with the original conditions. Cancel factors or exploit structure when doing so is faster and more reliable than decimal entry.
11 / UNDERSTAND & APPLY
Questions referring to the bookstall use the January–March counts above; the other questions identify their display or numerical data.
ORIGINAL PRACTICE · 1
150
Add the fiction column: 40+50+60=150. Adding all row totals would include nonfiction too.
ORIGINAL PRACTICE · 2
B
Shares are 30/70=3/7, 20/70=2/7, and 40/100=2/5. February has the smallest share. Raw nonfiction counts alone would not always settle this if totals differed substantially.
ORIGINAL PRACTICE · 3
A, B, C and E
A: (50−40)/40=25%. B: both totals are 70. C: 40=2·20. E: increases are 10 and 10. D is false because the 30-book increase is based on 70, giving about 42.9%, not 30%.
ORIGINAL PRACTICE · 4
540
0.30·1800=540. The angle 108° is another representation of the share, not a currency amount.
ORIGINAL PRACTICE · 5
7
The first two bins total 2+5=7. The third begins at 20 and is excluded from “below 20.”
ORIGINAL PRACTICE · 6
D: median 9
The five-number summary explicitly supplies the median. The other quantities depend on details the summary does not retain.
ORIGINAL PRACTICE · 7
4
Read the provided pair (5,4). Following a smooth upward trend instead would miss the actual observed point.
ORIGINAL PRACTICE · 8
A, C and E
The broad tendency supports A, the observed maximum is 7, and (4,5) supports E. B fails between 4 and 5 hours, where points fall from 5 to 4. D overstates what observational association establishes.
KEEP THE BIG IDEAS
READ WITH CONTEXT
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