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).

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.

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.

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.

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.

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).

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.

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.

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.

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.

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)!].

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.

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).

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.

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.

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.

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.

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.

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.

What is the formula for Circular Permutations of n distinct items?

Circular Permutations = (n - 1)!. One position is fixed to remove rotational symmetry.

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

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.

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.

Level: intermediate
Languages: en → en
Cards: 32
Markdown: GRE Quantitative Reasoning: Data Interpretation, Normal Distribution & Probability (.md)

Flashcards (32)

#	Front (Term / Question)	Back (Definition / Answer)
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 ± 1sigma). • ~95.4% of data falls within 2 standard deviations (mu ± 2sigma). • ~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 = (w1x1 + w2x2 + ... + 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 + 1sigma, and mu + 2sigma in a normal distribution?	• mu (Mean / Median): 50th percentile. • mu + 1sigma: ~84.1th percentile (50% + 34.1%). • mu + 2sigma: ~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.