Descriptive Statistics
Descriptive statistics is the GRE's favourite way to test whether you actually understand a set of numbers or just know how to average them. Three measures of centre — mean, median and mode — plus the simplest measure of spread, the range, cover the bulk of what appears, and the test almost never asks for a raw calculation. Instead it asks what happens to the median when you add a value, whether the mean or the median is larger for a skewed set, or how to back out a missing number when the average is given. Because the on-screen calculator is basic, the winning approach is conceptual: know exactly what each measure is sensitive to, and you can answer most questions — especially Quantitative Comparison — without adding a single long column.
Topics
⚡ GRE shortcuts & speed methods
The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.
- Convert a target average into a required TOTAL (sum = mean × n) before doing anything else — most "what score is needed" questions collapse to one subtraction.
- Sort before you read the median. The commonest error is taking the middle of the unsorted list.
- Adding or subtracting the same constant to every value shifts the mean and median by that constant but leaves the range and standard deviation unchanged.
- A new value equal to the current mean leaves the mean fixed — a fast Quantitative Comparison shortcut.
- For skewed data, the tail pulls the mean: a high outlier makes mean > median; a low outlier makes mean < median.
- Weighted averages lean toward the group with the larger weight — never average the sub-averages directly.
- Multiplying every value by k multiplies the mean, median AND range by k.
⚠️ Common mistakes & traps
GRE is designed so that careless errors here cost you marks. Internalise each trap before the exam.
- Averaging two group averages directly instead of weighting them by group size.
- Reading the median off an unsorted list.
- Assuming a change to one value moves the median — often it moves the mean while the median stays put.
- Thinking "the mean is unchanged" implies "the median is unchanged" (adding a value equal to the mean can still shift the median).
- Forgetting that adding a constant to every value leaves the range and standard deviation unchanged.
- Treating the range as robust — a single outlier can swing it wildly while the median barely moves.
📈 GRE exam insight & question patterns
Quantitative Comparison — Column A: the mean of 2, 4, 6, 8, 100. Column B: the median of the same set. Which is greater?
Column A. Mean = 120/5 = 24; median = 6. The outlier 100 lifts the mean far above the median.
Numeric Entry — A student has scored 84, 78 and 90. What must the fourth score be for an average of 85?
Required total = 85 × 4 = 340; scored so far 252; needed = 88.
Data Interpretation — A set of five values has mean 40. If one value of 60 is removed, what is the mean of the remaining four?
Old total = 200; remove 60 → 140 over 4 values → 35.
Multiple-answer — Which statistics are unchanged when 10 is added to every value of a data set? (range, mean, median, standard deviation)
Range and standard deviation. The mean and median each rise by 10; spread is unaffected.
🎴 Flashcards — instant recall
Tap a card to reveal the answer. Drill these until they are automatic.
📌 Quick revision
- Mean uses every value and is dragged by outliers; median is positional and robust; mode is the most frequent value.
- Always sort before finding a median; for an even count, average the two middle values.
- Range = max − min and is highly sensitive to a single outlier.
- Weight sub-averages by their counts — never average averages directly.
- Missing-value problems: convert the target mean into a required total, then subtract.
- Changing one value shifts the mean by (change)/n but often leaves the median untouched.
- Adding a constant to every value shifts centre but not spread; multiplying scales both.
- Most GRE questions here — especially Quantitative Comparison — are reasoning, not calculation.
Chapter test
🏆 Vidaara GRE success checklist
You have truly mastered Descriptive Statistics 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 checkpoint | Target |
|---|---|
| Concept theory & formulas understood | 100% |
| Topic practice sets attempted (4 topics) | 4/4 |
| Best topic-test score | — → 80%+ |
| Chapter test score | — → 80%+ |
| Flashcards drilled to instant recall | 8 cards |
Formula Reference Sheet
Measures of centre
| Arithmetic mean | mean = (sum of values) / (number of values) |
|---|---|
| Sum from the mean | sum = mean × n |
| Median (odd n) | the single middle value once sorted |
| Median (even n) | average of the two middle values once sorted |
| Mode | the value(s) that occur most often |
Spread & weighting
| Range | range = greatest value − least value |
|---|---|
| Weighted mean | (Σ weightᵢ × valueᵢ) / (Σ weightᵢ) |
| Missing value | missing = (target mean × n) − (known sum) |
| New mean after adding x | (old sum + x) / (n + 1) |