# GRE Quantitative Reasoning: Data Interpretation, Normal Distribution & Probability

> 32 GRE Quantitative Reasoning review cards on the empirical normal distribution rule, z-scores, boxplots, percentiles, standard deviation, permutations and combinations, conditional and independent probability, and chart interpretation.

- **Canonical URL:** https://flashcards.world/flashcards/sets/1703de1e-5244-44af-a85f-bf88aaa60f5a/
- **Markdown URL:** https://flashcards.world/flashcards/sets/1703de1e-5244-44af-a85f-bf88aaa60f5a.md
- **Level:** intermediate
- **Languages:** en → en
- **Total Cards:** 32

## Flashcards (32 Cards)

| # | Front (Term / Prompt) | Back (Definition / Answer) | Example | Multiple-Choice Options |
| :--- | :--- | :--- | :--- | :--- |
| 1 | How do you calculate combinations when selecting a committee with 'At least one' member from group A? | Complementary Counting: (Total possible committees without restriction) - (Committees formed with ZERO members from group A). |  |  |
| 2 | How do you compare Standard Deviations of two data sets by visual inspection? | Look at the dispersion of data points relative to their mean. A set whose values are clustered tightly around its center has a smaller SD; a set whose values are concentrated far at the extremes has a larger SD. |  |  |
| 3 | What is the Fundamental Counting Principle for compound events? | If task 1 can be done in n1 ways, task 2 in n2 ways, and task k in nk ways, the total number of ways to perform the sequence of tasks is n1 * n2 * ... * nk. |  |  |
| 4 | What is the symmetry property of Combinations C(n, k)? | C(n, k) = C(n, n - k). Choosing k items to select is identical to choosing (n - k) items to reject. |  |  |
| 5 | What happens to the Mean and Median in a Right-Skewed distribution? | Mean > Median. Extreme high outliers in the long right tail drag the arithmetic mean upward, while the median remains resistant. |  |  |
| 6 | What is the effect on Standard Deviation if 15 is added to every number in a data set? | The standard deviation is completely UNCHANGED (adding a constant shifts the center without changing the spread). |  |  |
| 7 | What is the probability formula for Mutually Exclusive events? | P(A and B) = 0. Therefore, P(A or B) = P(A) + P(B). Mutually exclusive events cannot occur simultaneously. |  |  |
| 8 | What happens to the Mean and Median in a Left-Skewed distribution? | Mean < Median. Extreme low outliers in the long left tail pull the arithmetic mean downward below the median. |  |  |
| 9 | How many 3-digit positive integers can be formed from digits {1, 2, 3, 4, 5} if repetition IS allowed? | 5 * 5 * 5 = 5^3 = 125 integers. |  |  |
| 10 | What is the Expected Value E(X) formula for a discrete probability distribution? | E(X) = sum of [x_i * P(x_i)] for all outcomes x_i. It represents the long-term theoretical mean outcome. |  |  |
| 11 | What are the Permutation and Combination formulas on the GRE? | • Permutations (Order matters): P(n, k) = n! / (n - k)! • Combinations (Order does not matter): C(n, k) = n! / [k! * (n - k)!]. |  |  |
| 12 | What is the 'Truncated Y-Axis' visual trap in Data Interpretation bar charts? | A bar chart whose vertical axis begins at a non-zero baseline (e.g., starting at 90 instead of 0) visually exaggerates minor percentage differences between bars. |  |  |
| 13 | What is the 68-95-99.7 Empirical Rule for a Normal Distribution? | In any normal distribution with mean mu and standard deviation sigma: • ~68.2% of data falls within 1 standard deviation (mu ± 1*sigma). • ~95.4% of data falls within 2 standard deviations (mu ± 2*sigma). • ~99.7% of data falls within 3 standard deviations (mu ± 3*sigma). |  |  |
| 14 | How do you calculate probability when sampling without replacement? | Multiply sequential probabilities, reducing both the numerator and denominator after each draw. Example: P(2 Red balls from urn with 4 Red and 6 Blue) = (4/10) * (3/9) = 12/90 = 2/15. |  |  |
| 15 | What is the formula for Conditional Probability P(A \| B)? | P(A \| B) = P(A and B) / P(B), where P(B) > 0. It represents the probability that event A occurs restricted to the sample space of event B. |  |  |
| 16 | What is the Complement Rule for 'At least one' probability questions? | P(at least one success) = 1 - P(no successes) = 1 - P(all failures). Calculating the complement is almost always significantly faster. |  |  |
| 17 | What is the formula for a Weighted Average on GRE Quantitative sections? | Weighted Average = (w1*x1 + w2*x2 + ... + wn*xn) / (w1 + w2 + ... + wn). The average is pulled closer to the group with the larger weighting. |  |  |
| 18 | What is the IQR of a data set with Q1 = 18 and Q3 = 42? | IQR = Q3 - Q1 = 42 - 18 = 24. |  |  |
| 19 | What is the formula for the Z-score and what does it measure? | z = (x - mu) / sigma. It measures the exact number of standard deviations a given raw data point x lies above (if z > 0) or below (if z < 0) the population mean. |  |  |
| 20 | What is the formula for arranging n objects where some items are repeated (multiset permutations)? | Total permutations = n! / (p! * q! * r!...), where p, q, r are the frequencies of identical items. Example: Arranging letters in 'SUCCESS' (7 letters: 3 S, 2 C, 1 U, 1 E) = 7! / (3! * 2! * 1! * 1!) = 420. |  |  |
| 21 | What is the formula for Circular Permutations of n distinct items? | Circular Permutations = (n - 1)!. One position is fixed to remove rotational symmetry. |  |  |
| 22 | What is the General Addition Rule of probability for any two events A and B? | P(A or B) = P(A) + P(B) - P(A and B). The intersection P(A and B) is subtracted to prevent double-counting. |  |  |
| 23 | In Data Interpretation, how do you handle questions requiring estimation? | Scan the answer choices first. If choices are widely separated (e.g., 10%, 25%, 50%), round chart figures aggressively to rapid round numbers to save calculation time. |  |  |
| 24 | What is the mathematical definition of Independent Events in probability? | P(A and B) = P(A) * P(B). The occurrence of event A provides zero information regarding the likelihood of event B: P(A \| B) = P(A). |  |  |
| 25 | How many 3-digit positive integers can be formed from digits {1, 2, 3, 4, 5} if repetition is NOT allowed? | P(5, 3) = 5 * 4 * 3 = 60 integers. |  |  |
| 26 | What are the five summary statistics shown on a Boxplot (Box-and-Whisker Plot)? | 1. Minimum 2. First Quartile (Q1, 25th percentile) 3. Median (Q2, 50th percentile) 4. Third Quartile (Q3, 75th percentile) 5. Maximum. The box spans the Interquartile Range (IQR = Q3 - Q1), representing the middle 50% of data. |  |  |
| 27 | What are the percentile ranks for mu, mu + 1*sigma, and mu + 2*sigma in a normal distribution? | • mu (Mean / Median): 50th percentile. • mu + 1*sigma: ~84.1th percentile (50% + 34.1%). • mu + 2*sigma: ~97.7th percentile (50% + 34.1% + 13.6%). • mu - 1*sigma: ~15.9th percentile. |  |  |
| 28 | What is the relationship between Variance and Standard Deviation? | Variance = (Standard Deviation)^2. For a population of N values (the default convention on the GRE), sigma = sqrt[(1/N) * sum((x_i - mu)^2)], whereas sample standard deviation divides by n - 1. |  |  |
| 29 | What is the definition of the p-th Percentile in GRE Data Interpretation? | The value below which p percent of the observations in the dataset fall. If an applicant scores in the 85th percentile, they scored higher than 85% of all test-takers. |  |  |
| 30 | What is the effect on Standard Deviation if every number in a data set is multiplied by -3? | The standard deviation is multiplied by \|-3\| = 3. Standard deviation is always a non-negative scalar. |  |  |
| 31 | What is the probability of rolling an even number on both rolls when a fair 6-sided die is rolled twice? | On each independent roll of a fair 6-sided die, P(Even) = 3/6 = 1/2. Therefore, P(Even on Roll 1 and Even on Roll 2) = (1/2) * (1/2) = 1/4. |  |  |
| 32 | What is the ratio of combinations identity C(n, k) / C(n, k - 1)? | C(n, k) / C(n, k - 1) = (n - k + 1) / k. |  |  |

---
Study this deck interactively with FSRS-6 spaced repetition, audio review, and multiple-choice mode at [Flashcards World](https://flashcards.world/flashcards/sets/1703de1e-5244-44af-a85f-bf88aaa60f5a/).