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Questions and Answers
If event A is a subset of event B, which of the following is true?
If event A is a subset of event B, which of the following is true?
The intersection of two disjoint events is always an empty set.
The intersection of two disjoint events is always an empty set.
True
What is the probability of an impossible event?
What is the probability of an impossible event?
0
The complement of an event A consists of all outcomes in the sample space that are ______ in A.
The complement of an event A consists of all outcomes in the sample space that are ______ in A.
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Match the set notations with their descriptions:
Match the set notations with their descriptions:
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Given a sample space of a fair six-sided die, what is the probability of rolling an even number?
Given a sample space of a fair six-sided die, what is the probability of rolling an even number?
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The probability of the union of two events is always equal to the sum of their individual probabilities.
The probability of the union of two events is always equal to the sum of their individual probabilities.
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Using the formula for the probability of a union of two events with the formula $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, if $P(A) = 0.45$, $P(B) = 0.35$, and $P(A \cap B) = 0.1$, what is the value of $P(A \cup B)$?
Using the formula for the probability of a union of two events with the formula $P(A \cup B) = P(A) + P(B) - P(A \cap B)$, if $P(A) = 0.45$, $P(B) = 0.35$, and $P(A \cap B) = 0.1$, what is the value of $P(A \cup B)$?
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Which of the following is NOT a measure of central tendency?
Which of the following is NOT a measure of central tendency?
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The arithmetic mean is not affected by extreme values.
The arithmetic mean is not affected by extreme values.
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What property of the arithmetic mean makes it easy to calculate for any sample?
What property of the arithmetic mean makes it easy to calculate for any sample?
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Measures of central tendency describe where the data are ______.
Measures of central tendency describe where the data are ______.
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Given the numbers 2, 4, 6, 8, and 10, what is the arithmetic mean?
Given the numbers 2, 4, 6, 8, and 10, what is the arithmetic mean?
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A student has test scores of 75, 80, and 90. What score does the student need on the next test to achieve an average of 85?
A student has test scores of 75, 80, and 90. What score does the student need on the next test to achieve an average of 85?
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Match the following terms with their descriptions:
Match the following terms with their descriptions:
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For a given set of data, there can be multiple arithmetic means.
For a given set of data, there can be multiple arithmetic means.
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What does IQR stand for?
What does IQR stand for?
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The coefficient of variation is a unit-dependent measure.
The coefficient of variation is a unit-dependent measure.
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In a box of 100 transistors, 20 are defective. If event A is selecting a defective transistor, what is P(A)?
In a box of 100 transistors, 20 are defective. If event A is selecting a defective transistor, what is P(A)?
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If the first quartile (Q1) is 10 and the third quartile (Q3) is 25, what is the interquartile range (IQR)?
If the first quartile (Q1) is 10 and the third quartile (Q3) is 25, what is the interquartile range (IQR)?
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If events A and B are independent, then P(A ∩ B) = P(A) + P(B).
If events A and B are independent, then P(A ∩ B) = P(A) + P(B).
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The interpercentile range (IPR) is the difference between two _________.
The interpercentile range (IPR) is the difference between two _________.
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Given P(A ∩ B) = 15/100 and P(B) = 60/100, what is P(A|B)?
Given P(A ∩ B) = 15/100 and P(B) = 60/100, what is P(A|B)?
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In a dataset, if the position of Q3 is calculated to be 5.25, what value is typically used to find Q3?
In a dataset, if the position of Q3 is calculated to be 5.25, what value is typically used to find Q3?
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Name two of the three counting techniques used to determine the number of outcomes of an experiment.
Name two of the three counting techniques used to determine the number of outcomes of an experiment.
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If P(A) = 1/3 and P(B) = 1/2 and A and B are independent, then P(A∩B) is ______.
If P(A) = 1/3 and P(B) = 1/2 and A and B are independent, then P(A∩B) is ______.
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In the transistor example, given that P(A ∩ B) = 15/100 and P(A) = 20/100, what is P(B|A)?
In the transistor example, given that P(A ∩ B) = 15/100 and P(A) = 20/100, what is P(B|A)?
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Given a dataset, which of the following indicates greater dispersion?
Given a dataset, which of the following indicates greater dispersion?
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Match the following concepts with their appropriate formula:
Match the following concepts with their appropriate formula:
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If the two events A and B are independent, then P(A|B) = P(A).
If the two events A and B are independent, then P(A|B) = P(A).
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Match each probability notation to its correct definition:
Match each probability notation to its correct definition:
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Which of the following statements is true regarding the t-distribution?
Which of the following statements is true regarding the t-distribution?
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The shape of the t-distribution is independent of the sample size.
The shape of the t-distribution is independent of the sample size.
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When using the t-distribution, what happens to its shape as the sample size increases?
When using the t-distribution, what happens to its shape as the sample size increases?
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For a Chi-Square distribution, the curve is skewed to the ______.
For a Chi-Square distribution, the curve is skewed to the ______.
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Match the following distributions with their key properties:
Match the following distributions with their key properties:
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Given a t-distribution, if $P(t \geq 2.571) = 0.025$, what is the probability $P(t < 2.571)$?
Given a t-distribution, if $P(t \geq 2.571) = 0.025$, what is the probability $P(t < 2.571)$?
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If a sample of 4 cats is chosen at random from a population with an average weight of 12 pounds and a standard deviation of 8 pounds, and the sample average was found to be 7 pounds, what is the t-score calculated?
If a sample of 4 cats is chosen at random from a population with an average weight of 12 pounds and a standard deviation of 8 pounds, and the sample average was found to be 7 pounds, what is the t-score calculated?
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The chi-square distribution has degrees of freedom that are calculated based on the population mean.
The chi-square distribution has degrees of freedom that are calculated based on the population mean.
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Given events A and B, if $P(A) = 0.5$, $P(B) = 0.25$, and $P(A \cap B) = 0.2$, what is $P(A \cup B)$?
Given events A and B, if $P(A) = 0.5$, $P(B) = 0.25$, and $P(A \cap B) = 0.2$, what is $P(A \cup B)$?
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If two events A and B are disjoint, then $P(A \cap B) = 1$.
If two events A and B are disjoint, then $P(A \cap B) = 1$.
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If a fair die is rolled twice, how many possible outcomes are there?
If a fair die is rolled twice, how many possible outcomes are there?
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If $P(A) = 0.7$, then $P(A^\prime) = $ ______.
If $P(A) = 0.7$, then $P(A^\prime) = $ ______.
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Match the following probabilities with their meanings given $P(A) = 0.6$, $P(B) = 0.3$ and $P(A \cap B) = 0.1$.
Match the following probabilities with their meanings given $P(A) = 0.6$, $P(B) = 0.3$ and $P(A \cap B) = 0.1$.
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If $P(A) = 0.5$, $P(B) = 0.25$ and $P(A \cap B) = 0.2$, what is $P(A^\prime \cup B^\prime)$?
If $P(A) = 0.5$, $P(B) = 0.25$ and $P(A \cap B) = 0.2$, what is $P(A^\prime \cup B^\prime)$?
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If events A and B are not disjoint, then $P(A \cap B)$ must be greater than zero.
If events A and B are not disjoint, then $P(A \cap B)$ must be greater than zero.
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A balanced coin is tossed 5 times. How many possible outcomes are there?
A balanced coin is tossed 5 times. How many possible outcomes are there?
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The formula for conditional probability $P(A|B)$ is $P(A \cap B) / $ ______.
The formula for conditional probability $P(A|B)$ is $P(A \cap B) / $ ______.
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Given two events A and B with $P(A|B) = 0.4$ and $P(A \cap B) = 0.2$, what is $P(B)$?
Given two events A and B with $P(A|B) = 0.4$ and $P(A \cap B) = 0.2$, what is $P(B)$?
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Study Notes
Descriptive Statistical Measures
- Measures of central tendency describe the location of data.
- Common measures include arithmetic mean, median, and mode.
Arithmetic Mean
- The sample mean (average) is calculated by summing all data points and dividing by the total number of data points.
- Formula: X = (X₁ + X₂ + ... + Xₙ) / n
Examples of Arithmetic Mean Calculations
- The mean of 9, 3, 7, 3, 8, 10, 2 is 6
- The average of 96, 94, 72, 52, 56 marks is 74
Properties of Arithmetic Mean
- A unique mean exists for a given dataset
- Easy to calculate
- Affected by extreme values, making it potentially not entirely representative of the majority of data
Median
- The median is the middle value in a sorted dataset.
- In an odd-sized dataset, the median is the middle value.
- In an even-sized dataset, the median is the average of the two middle values.
Mode
- The mode is the most frequently occurring value in a dataset.
- A dataset can have multiple modes or no mode.
Measures of Variation (Dispersion)
- Dispersion statistics summarize the spread or scatter of data.
- Common measures of dispersion include range, variance, standard deviation, interquartile range, and interpercentile range.
Range
- Range = maximum observation – minimum observation
Examples of Range Calculations
- Range of 13, 18, 13, 14, 16, 14, 21, 13 is 8
- If Jordan's hottest temperature was 39.2° and range is 40.7°, the coldest temp is -1.5°
Variance
- Formula for sample variance S2 = Σᵢ=₁ (xᵢ-X)² / (n-1) Where: xᵢ = each data point X = sample mean n = total number of values
Standard Deviation
- Standard deviation is the square root of the variance.
- Formula: √S² = s
Quartiles, Deciles, and Percentiles
- Quartiles divide data into four equal parts.
- First quartile (Q1) is the 25th percentile.
- Second quartile (Q2) is the 50th percentile, which is the median.
- Third quartile (Q3) is the 75th percentile.
- Deciles divide data into 10 equal parts.
- Percentiles divide data into 100 equal parts.
Interquartile Range (IQR)
- IQR = Q3 − Q1
Interpercentile Range (IPR)
- IPR = pₙ − pₘ Where pₙ and pₘ represent the nth and mth percentile, respectively
Coefficient of Variation (CV)
- Formula: CV = (s / x̄) * 100 Where s = sample standard deviation and x̄ = sample mean
Counting Techniques
- Product rule: The total number of ways to complete a sequence of steps is the product of the number of ways to complete each step if the choice of each step is not conditional upon previous steps.
- Permutations: An arrangement of objects where order matters without repetition
- Combinations: An arrangement of objects where order does not matter without repetition
Factorials
- n! (n factorial) is the product of all positive integers less than or equal to n.
- 0! = 1
Sample Space and Events
- Sample space (Ω) is the set of all possible outcomes of a random experiment.
- An event is a subset of the sample space.
- Empty set (Ø) and the sample space (Ω) are considered events.
Conditional Probability
- The probability of event A given event B is P(A|B) = P(A ∩ B) / P(B) P(A|B) = Probability of event A occurring given event B occurred
Independent Events
- A and B are independent if and only if P(A ∩ B) = P(A)P(B)
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Description
Explore the fundamental concepts of descriptive statistics through this quiz. Focus on measures of central tendency, including arithmetic mean, median, and mode. Understand how to calculate these measures and their significance in data analysis.
