GRE Quant · Study & Practice

Standard Deviation, Quartiles & Percentiles

AreaData Analysis DifficultyMedium GRE weightageMedium–High — spread, percentiles and boxplots recur; standard deviation is tested by reasoning, not hand-calculation

This chapter is about spread — how stretched out a data set is — and it trips up test-takers who expect to compute. Here is the liberating truth: the GRE almost never asks you to hand-calculate a standard deviation. It asks which of two sets has the larger spread, what happens to the SD when you add a constant, or how the 68-95-99.7 rule places a value on a normal curve. Alongside SD sit the positional measures — quartiles, the interquartile range, percentiles and the boxplot — which describe spread by rank rather than by distance from the mean. Master the ideas: SD measures typical distance from the mean, adding a constant never changes spread, and percentiles are about rank, not score. Do that and you handle every question this topic throws at you, including the Quantitative Comparisons that look computational but are pure reasoning.

Topics

1 Spread & Standard Deviation 4 worked · 5 practice · 8-Q test Start → 2 Quartiles & the Interquartile Range 4 worked · 5 practice · 8-Q test Start → 3 Percentiles 4 worked · 5 practice · 8-Q test Start → 4 Boxplots 4 worked · 5 practice · 8-Q test Start →

⚡ GRE shortcuts & speed methods

The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.

  • Adding a constant to every value leaves the standard deviation (and IQR and range) unchanged — a one-line Quantitative Comparison answer.
  • Multiplying every value by k multiplies the SD, IQR and range by |k|.
  • To compare two SDs, judge how tightly each set clusters around its mean — do not compute.
  • A set with all identical values has SD exactly 0; that is the smallest possible spread.
  • Quartile landmarks: Q1 = 25th percentile, median = 50th, Q3 = 75th.
  • On a boxplot each of the four regions holds about 25% of the data — width shows spread, not count.
  • For the 68-95-99.7 rule: about 68% within 1 SD, 95% within 2 SD, 99.7% within 3 SD of the mean.

⚠️ Common mistakes & traps

GRE is designed so that careless errors here cost you marks. Internalise each trap before the exam.

  • Trying to hand-calculate a standard deviation — the GRE tests the concept and comparisons, not the arithmetic.
  • Believing a constant shift changes the SD; it changes the mean but never the spread.
  • Confusing a percentile (rank) with a percentage score (fraction correct).
  • Assuming a wide boxplot section holds more data — it holds the same ~25%, just more spread out.
  • Forgetting to sort before finding quartiles.
  • Reading the whiskers as showing how many outliers there are rather than just their reach.

📈 GRE exam insight & question patterns

Quantitative Comparison — Column A: SD of {3, 5, 7}. Column B: SD of {103, 105, 107}. Which is greater?

They are equal. The second set is the first with 100 added, and a constant shift never changes the SD.

Data Interpretation — A boxplot shows min 8, Q1 14, median 18, Q3 26, max 40. What is the IQR?

IQR = Q3 − Q1 = 26 − 14 = 12.

Concept — A student is in the 88th percentile on the GRE. What does that mean?

About 88% of test-takers scored at or below that student — it is a rank, not a fraction of questions correct.

Numeric Entry — On a normal distribution, about what percent of values fall within 2 standard deviations of the mean?

By the 68-95-99.7 rule, about 95%.

🎴 Flashcards — instant recall

Tap a card to reveal the answer. Drill these until they are automatic.

Standard deviation (meaning)Tap to reveal
typical distance of values from the mean
Add a constant to every valueTap to reveal
SD unchanged; mean shifts
Multiply every value by kTap to reveal
SD is multiplied by |k|
SD = 0 when…Tap to reveal
every value is identical
IQRTap to reveal
Q3 − Q1 (spread of the middle 50%)
Q1, Q2, Q3 as percentilesTap to reveal
25th, 50th (median), 75th
PercentileTap to reveal
the value below which about k% of the data falls (rank, not score)
Boxplot five-number summaryTap to reveal
min, Q1, median, Q3, max
68-95-99.7 ruleTap to reveal
≈68% / 95% / 99.7% within 1 / 2 / 3 SD of the mean

📌 Quick revision

  • Standard deviation measures typical distance from the mean — the GRE tests it by comparison, not hand-calculation.
  • Adding a constant to every value never changes the SD, IQR or range; multiplying by k scales all three by |k|.
  • A constant data set has SD zero — the minimum possible spread.
  • Quartiles cut sorted data into four equal-count parts; IQR = Q3 − Q1 describes the robust middle 50%.
  • Percentiles are about rank, not raw score: Q1/median/Q3 are the 25th/50th/75th percentiles.
  • A boxplot draws the five-number summary; each of its four regions holds about 25% of the data.
  • The 68-95-99.7 rule places values on a normal curve without any calculation.

Chapter test

📝 Standard Deviation, Quartiles & Percentiles — Chapter Test
25 fresh questions · timed · full solutions
Start chapter test →
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🏆 Vidaara GRE success checklist

You have truly mastered Standard Deviation, Quartiles & Percentiles when you can tick every box below.

  • Recall every formula in this chapter without looking them up
  • Solve each topic’s practice set with at least 80% accuracy
  • Use the chapter shortcuts to cut your solving time in half
  • Spot and avoid every common trap listed above
  • Score 80%+ on the timed chapter test

📋 Chapter mastery scorecard

Track where you stand. Aim for the target before moving to the next chapter.

Skill checkpointTarget
Concept theory & formulas understood100%
Topic practice sets attempted (4 topics)4/4
Best topic-test score— → 80%+
Chapter test score— → 80%+
Flashcards drilled to instant recall9 cards