Graduate Record Examinations (GRE) Quantitative Reasoning: Data Analysis and Test Strategy Syllabus

Quantitative Reasoning: Data Analysis and Test Strategy syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Reasoning: Data Analysis and Test Strategy in Graduate Record Examinations (GRE), not a summary of it.

1. 1

   Descriptive Statistics

   3 topics

   • Measures of central tendency
     • Mean, median and mode
     • Weighted averages
   • Measures of spread
     • Range and interquartile range
     • Standard deviation and variance
   • Distributions
     • Normal distribution and percentiles
     • Quartiles and percentile ranks
2. 2

   Probability and Counting

   3 topics

   • Basic probability rules
     • Independent and dependent events
     • Mutually exclusive events
     • Complementary events
   • Combinations and permutations
     • Counting principle
     • Order versus selection
   • Sets and Venn diagrams
     • Union, intersection and complement
     • Overlapping group problems
3. 3

   Data Interpretation

   3 topics

   • Reading tables and graphs
     • Bar, line and circle graphs
     • Frequency distributions and boxplots
   • Multi-question data sets
     • Cross-referencing multiple displays
   • Calculations from data displays
     • Percentages and ratios from charts
4. 4

   Question Formats and Strategy

   4 topics

   • Quantitative comparison questions
     • The four fixed answer choices
     • Plugging in values strategy
   • Multiple-choice and numeric entry
     • Single and multiple answer formats
     • Entering fractions and decimals
   • Using the on-screen calculator
     • When to calculate versus estimate
   • Section-level test mechanics
     • Section-adaptive design across two sections
     • Mark-and-review and pacing

Quantitative Reasoning: Data Analysis and Test Strategy flashcards for Graduate Record Examinations (GRE)

18 of 51 cards from the Quantitative Reasoning: Data Analysis and Test Strategy deck — real questions with worked answers.

1. What is the arithmetic mean of a data set, and what is its formula?

   The mean is the average: the sum of all values divided by the count of values. For values $x_1, x_2, \dots, x_n$: $$\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i$$

2. How do you find the median of a data set?

   Order the values from least to greatest. With an odd count, the median is the middle value. With an even count $n$, it is the mean of the two middle values (positions $\frac{n}{2}$ and $\frac{n}{2}+1$).

3. What is the mode of a data set?

   The value (or values) that occurs most frequently. A set can have no mode, one mode, or several modes (bimodal, multimodal).

4. When data is skewed, how do the mean and median compare?

   In a right-skewed (positive) distribution the mean is pulled above the median; in a left-skewed (negative) distribution the mean is pulled below the median. The median resists outliers, the mean does not.

5. What is the range of a data set?

   The difference between the greatest and least values: $$\text{range} = x_{\max} - x_{\min}$$ It measures spread but is highly sensitive to outliers.

6. How are the quartiles $Q_1$, $Q_2$, $Q_3$ defined, and what is the interquartile range?

   $Q_1$ is the median of the lower half, $Q_2$ is the overall median, $Q_3$ is the median of the upper half. The interquartile range is $$\text{IQR} = Q_3 - Q_1$$ containing the middle 50% of the data.

7. What is the formula for the population standard deviation?

   $$\sigma = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2}$$ It is the square root of the variance and measures typical distance from the mean.

8. How is variance related to standard deviation?

   Variance is the square of the standard deviation: $\sigma^2$. It is the mean of the squared deviations from the mean. Standard deviation $\sigma = \sqrt{\sigma^2}$ returns to the original units.

9. If every value in a data set is increased by a constant $c$, how do the mean and standard deviation change?

   The mean increases by $c$. The standard deviation is unchanged, because adding a constant shifts all values equally without changing their spread.

10. If every value in a data set is multiplied by a constant $k>0$, how do the mean and standard deviation change?

    Both the mean and the standard deviation are multiplied by $k$: new mean $= k\bar{x}$, new standard deviation $= k\sigma$.

11. In a normal distribution, what percentages fall within 1, 2, and 3 standard deviations of the mean (the empirical rule)?

    Approximately 68% within $\pm 1\sigma$, 95% within $\pm 2\sigma$, and 99.7% within $\pm 3\sigma$ of the mean.

12. In the GRE's standard normal model, what approximate percentages lie in each of the six half-standard-deviation bands used on the test?

    Roughly 34% in each band within $1\sigma$ (about 34, 34), 14% in each band between $1\sigma$ and $2\sigma$, and 2% in each band between $2\sigma$ and $3\sigma$: about $2\%, 14\%, 34\%, 34\%, 14\%, 2\%$.

13. What are the key features of a normal distribution's shape?

    It is symmetric and bell-shaped about its mean. The mean, median, and mode are all equal and located at the center.

14. What is a percentile, and what does the 75th percentile represent?

    A percentile indicates the value below which a given percentage of data falls. The 75th percentile is the value at or below which 75% of the data lies; it equals $Q_3$.

15. How do you compute a standardized score (z-score) for a value $x$?

    $$z = \frac{x - \mu}{\sigma}$$ It gives the number of standard deviations $x$ lies above (positive) or below (negative) the mean.

16. What is the probability of an event, expressed as a ratio?

    For equally likely outcomes: $$P(E) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}}$$ Probabilities satisfy $0 \leq P(E) \leq 1$.

17. What is the complement rule in probability?

    The probability that an event does not occur is $$P(\text{not } E) = 1 - P(E)$$

18. State the addition rule for the probability of $A$ or $B$.

    $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ If $A$ and $B$ are mutually exclusive, $P(A \cap B)=0$, so $P(A \cup B) = P(A) + P(B)$.

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