How does probability calculation change when sampling without replacement?

Both the numerator and the denominator decrease on consecutive draws. Example: Drawing 2 aces from a 52-card deck: P(Ace 1) = 4/52; P(Ace 2 | Ace 1) = 3/51; Total = (4/52) * (3/51).

What is the 'carry-over' trap in Data Sufficiency?

Carrying information from Statement 1 into Statement 2. You must evaluate Statement 2 in complete isolation from Statement 1 before combining them in Choice C.

What is the relationship between Mean and Median in a Left-Skewed (negatively skewed) distribution?

Mean < Median. Extreme low values in the left tail drag the mean downward below the median.

What is the relationship between Variance and Standard Deviation?

Variance = (Standard Deviation)^2, and SD = sqrt(Variance). While SD is expressed in the original units of measurement, variance is expressed in squared units.

In a perfectly symmetrical unimodal distribution, what is the relationship between Mean and Median?

Mean = Median. If the distribution is also bell-shaped, Mean = Median = Mode at the central peak.

What is the mathematical definition of independent events in probability?

Events A and B are independent if the occurrence of one does not alter the probability of the other: P(A and B) = P(A) * P(B). Also, P(A | B) = P(A).

What is the Complement Rule for 'at least one' probability questions?

P(at least one occurrence) = 1 - P(zero occurrences). Whenever a problem asks for the probability of 'at least one success', calculating 1 - P(all failures) is almost always much faster.

What is the formula for the Expected Value E(X) of a discrete random variable?

E(X) = sum of [x_i * P(x_i)] for all possible outcomes x_i. It represents the long-run weighted average outcome.

What is the relationship between Mean and Median in a Right-Skewed (positively skewed) distribution?

Mean > Median. Extreme high values in the right tail pull the mean upward, while the median remains closer to the bulk of the data.

What is the general Addition Rule for the union of 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 GMAT Data Sufficiency, are diagrams drawn to scale?

NO! Diagrams in Data Sufficiency are deliberately NOT drawn to scale unless explicitly stated. You cannot infer right angles, parallel lines, or relative lengths from appearance.

What is the formula for the weighted average of two groups and which group does it favor?

Weighted Average = (w1*x1 + w2*x2) / (w1 + w2). The weighted average is always pulled closer to the group with the larger weight/frequency, dividing the distance between x1 and x2 in the inverse ratio of their weights.

In Data Sufficiency, what constitutes 'Sufficient' for a Yes/No question?

A statement is sufficient if the answer is a DEFINITE YES or a DEFINITE NO. If the answer is 'maybe' (sometimes yes, sometimes no), the statement is NOT sufficient. A definite 'NO' is sufficient!

How do outliers affect the mean versus the median?

• The mean is heavily sensitive to outliers (pulled in the direction of the extreme value). • The median is robust/resistant to outliers (it depends only on the rank order of values, not their extreme magnitude).

In GMAT Data Insights Multi-Source Reasoning, what is the best strategy for synthesis questions?

Check whether claims across different tabs confirm, qualify, or contradict each other. Never answer from memory; cross-reference specific metrics and definitions between tabs.

In Data Sufficiency, what constitutes 'Sufficient' for a Value question?

A statement is sufficient if and only if it leads to ONE AND ONLY ONE numerical value. If a statement yields two or more possible values (e.g., x = 2 or x = -3), it is NOT sufficient.

How does multiplying every number in a data set by a constant k affect mean, median, range, and standard deviation?

• Mean and Median are multiplied by k. • Range and Standard Deviation are multiplied by |k| (absolute value of k, since spread cannot be negative).

What is the conditional probability formula P(A | B)?

P(A | B) = P(A and B) / P(B), representing the probability that event A occurs given that event B has already occurred (where P(B) > 0).

How is the median determined for an ordered set of n numbers?

Arrange elements in ascending order: • If n is ODD, median is the single middle value at position (n + 1)/2. • If n is EVEN, median is the arithmetic mean of the two middle values at positions n/2 and (n/2) + 1.

How do you convert a ratio of boys to girls (a : b) into the probability of selecting a boy at random?

P(Boy) = a / (a + b). The denominator must be the sum of all ratio parts representing the total population.

What is the primary visual trap in Graphics Interpretation questions with dual vertical axes?

Failing to check which curve belongs to which axis! The left axis may have different units, scale intervals, or baselines compared to the right axis.

What is the two-group overlapping sets (Venn diagram) formula?

Total = Group A + Group B - (Both A and B) + Neither. Alternatively: Total = (Only A) + (Only B) + (Both) + (Neither).

What is the three-group overlapping sets formula for GMAT Data Insights?

Total = A + B + C - (sum of 2-group overlaps) + (all three groups) + Neither. Alternatively: Total = (Exactly 1) + (Exactly 2) + (Exactly 3) + Neither.

What is the probability rule for mutually exclusive events?

Events A and B are mutually exclusive if they cannot happen simultaneously: P(A and B) = 0. Therefore, P(A or B) = P(A) + P(B).

In GMAT Two-Part Analysis questions, what is the core solving workflow?

Identify the shared variable or mathematical constraint connecting both parts. Often, solving for one part constrains or directly gives the solution to the second part.

How do you find the median from a frequency histogram of n items?

Compute n/2. Accumulate bar frequencies from left to right until the cumulative frequency reaches or exceeds the position of the median.

What is the relationship between the arithmetic mean, sum of elements, and number of elements?

Mean = (Sum of all terms) / (Number of terms), which implies Sum = Mean * n. In GMAT problems, always convert statements about the mean into statements about the total sum.

How does adding a constant k to every number in a data set affect mean, median, range, and standard deviation?

• Mean and Median INCREASE by k. • Range and Standard Deviation remain UNCHANGED (the spread/dispersion of values relative to each other does not change).

In GMAT Data Insights Table Analysis, what is the primary navigation tactic?

Sort by the relevant column immediately! Sorting converts an unordered search into an ordered scan, allowing instant identification of medians, percentiles, top/bottom ranks, or thresholds.

What is the conceptual definition and minimum possible value of Standard Deviation (SD)?

SD measures the dispersion of data points around the mean. Minimum SD is 0, which occurs if and only if all numbers in the set are identical. SD can never be negative: SD >= 0.

What are mode and range in GMAT descriptive statistics?

• Mode: The value that appears with greatest frequency (a set can have no mode, one mode, or multiple modes). • Range: Maximum value - Minimum value. Range is sensitive to extreme values.

What is the probability of selecting items with replacement vs without replacement in urn problems?

• With replacement: Probabilities remain constant on each draw; events are independent. • Without replacement: Total available items decrease by 1 on each draw; events are dependent.

Statistics (Svenska) — Grundläggande (A1/A2) 2: Data Insights & Statistics/Probability

[Svenska] Statistics (Svenska): Mean, median, mode, range, standard deviation, weighted averages, overlapping sets (Venn diagrams), and fundamental probability rules for GMAT Data Insights.

Level: basic
Languages: sv → sv
Cards: 32
Markdown: Statistics (Svenska) — Grundläggande (A1/A2) 2: Data Insights & Statistics/Probability (.md)

Flashcards (32)

#	Front (Term / Question)	Back (Definition / Answer)
1	How does probability calculation change when sampling without replacement?	Both the numerator and the denominator decrease on consecutive draws. Example: Drawing 2 aces from a 52-card deck: P(Ace 1) = 4/52; P(Ace 2 \| Ace 1) = 3/51; Total = (4/52) * (3/51).
2	What is the 'carry-over' trap in Data Sufficiency?	Carrying information from Statement 1 into Statement 2. You must evaluate Statement 2 in complete isolation from Statement 1 before combining them in Choice C.
3	What is the relationship between Mean and Median in a Left-Skewed (negatively skewed) distribution?	Mean < Median. Extreme low values in the left tail drag the mean downward below the median.
4	What is the relationship between Variance and Standard Deviation?	Variance = (Standard Deviation)^2, and SD = sqrt(Variance). While SD is expressed in the original units of measurement, variance is expressed in squared units.
5	In a perfectly symmetrical unimodal distribution, what is the relationship between Mean and Median?	Mean = Median. If the distribution is also bell-shaped, Mean = Median = Mode at the central peak.
6	What is the mathematical definition of independent events in probability?	Events A and B are independent if the occurrence of one does not alter the probability of the other: P(A and B) = P(A) * P(B). Also, P(A \| B) = P(A).
7	What is the Complement Rule for 'at least one' probability questions?	P(at least one occurrence) = 1 - P(zero occurrences). Whenever a problem asks for the probability of 'at least one success', calculating 1 - P(all failures) is almost always much faster.
8	What is the formula for the Expected Value E(X) of a discrete random variable?	E(X) = sum of [x_i * P(x_i)] for all possible outcomes x_i. It represents the long-run weighted average outcome.
9	What is the relationship between Mean and Median in a Right-Skewed (positively skewed) distribution?	Mean > Median. Extreme high values in the right tail pull the mean upward, while the median remains closer to the bulk of the data.
10	What is the general Addition Rule for the union of 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.
11	In GMAT Data Sufficiency, are diagrams drawn to scale?	NO! Diagrams in Data Sufficiency are deliberately NOT drawn to scale unless explicitly stated. You cannot infer right angles, parallel lines, or relative lengths from appearance.
12	What is the formula for the weighted average of two groups and which group does it favor?	Weighted Average = (w1x1 + w2x2) / (w1 + w2). The weighted average is always pulled closer to the group with the larger weight/frequency, dividing the distance between x1 and x2 in the inverse ratio of their weights.
13	In Data Sufficiency, what constitutes 'Sufficient' for a Yes/No question?	A statement is sufficient if the answer is a DEFINITE YES or a DEFINITE NO. If the answer is 'maybe' (sometimes yes, sometimes no), the statement is NOT sufficient. A definite 'NO' is sufficient!
14	How do outliers affect the mean versus the median?	• The mean is heavily sensitive to outliers (pulled in the direction of the extreme value). • The median is robust/resistant to outliers (it depends only on the rank order of values, not their extreme magnitude).
15	In GMAT Data Insights Multi-Source Reasoning, what is the best strategy for synthesis questions?	Check whether claims across different tabs confirm, qualify, or contradict each other. Never answer from memory; cross-reference specific metrics and definitions between tabs.
16	In Data Sufficiency, what constitutes 'Sufficient' for a Value question?	A statement is sufficient if and only if it leads to ONE AND ONLY ONE numerical value. If a statement yields two or more possible values (e.g., x = 2 or x = -3), it is NOT sufficient.
17	How does multiplying every number in a data set by a constant k affect mean, median, range, and standard deviation?	• Mean and Median are multiplied by k. • Range and Standard Deviation are multiplied by \|k\| (absolute value of k, since spread cannot be negative).
18	What is the conditional probability formula P(A \| B)?	P(A \| B) = P(A and B) / P(B), representing the probability that event A occurs given that event B has already occurred (where P(B) > 0).
19	How is the median determined for an ordered set of n numbers?	Arrange elements in ascending order: • If n is ODD, median is the single middle value at position (n + 1)/2. • If n is EVEN, median is the arithmetic mean of the two middle values at positions n/2 and (n/2) + 1.
20	How do you convert a ratio of boys to girls (a : b) into the probability of selecting a boy at random?	P(Boy) = a / (a + b). The denominator must be the sum of all ratio parts representing the total population.
21	What is the primary visual trap in Graphics Interpretation questions with dual vertical axes?	Failing to check which curve belongs to which axis! The left axis may have different units, scale intervals, or baselines compared to the right axis.
22	What is the two-group overlapping sets (Venn diagram) formula?	Total = Group A + Group B - (Both A and B) + Neither. Alternatively: Total = (Only A) + (Only B) + (Both) + (Neither).
23	What is the three-group overlapping sets formula for GMAT Data Insights?	Total = A + B + C - (sum of 2-group overlaps) + (all three groups) + Neither. Alternatively: Total = (Exactly 1) + (Exactly 2) + (Exactly 3) + Neither.
24	What is the probability rule for mutually exclusive events?	Events A and B are mutually exclusive if they cannot happen simultaneously: P(A and B) = 0. Therefore, P(A or B) = P(A) + P(B).
25	In GMAT Two-Part Analysis questions, what is the core solving workflow?	Identify the shared variable or mathematical constraint connecting both parts. Often, solving for one part constrains or directly gives the solution to the second part.
26	How do you find the median from a frequency histogram of n items?	Compute n/2. Accumulate bar frequencies from left to right until the cumulative frequency reaches or exceeds the position of the median.
27	What is the relationship between the arithmetic mean, sum of elements, and number of elements?	Mean = (Sum of all terms) / (Number of terms), which implies Sum = Mean * n. In GMAT problems, always convert statements about the mean into statements about the total sum.
28	How does adding a constant k to every number in a data set affect mean, median, range, and standard deviation?	• Mean and Median INCREASE by k. • Range and Standard Deviation remain UNCHANGED (the spread/dispersion of values relative to each other does not change).
29	In GMAT Data Insights Table Analysis, what is the primary navigation tactic?	Sort by the relevant column immediately! Sorting converts an unordered search into an ordered scan, allowing instant identification of medians, percentiles, top/bottom ranks, or thresholds.
30	What is the conceptual definition and minimum possible value of Standard Deviation (SD)?	SD measures the dispersion of data points around the mean. Minimum SD is 0, which occurs if and only if all numbers in the set are identical. SD can never be negative: SD >= 0.
31	What are mode and range in GMAT descriptive statistics?	• Mode: The value that appears with greatest frequency (a set can have no mode, one mode, or multiple modes). • Range: Maximum value - Minimum value. Range is sensitive to extreme values.
32	What is the probability of selecting items with replacement vs without replacement in urn problems?	• With replacement: Probabilities remain constant on each draw; events are independent. • Without replacement: Total available items decrease by 1 on each draw; events are dependent.