Descriptive Statistics and Introduction to Probability Practice Test

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• Which statement best differentiates a PMF from a PDF?
• State the central limit theorem in terms of the sampling distribution of the sample mean.
• What is the z-score for x = 85 if the distribution has mean μ = 100 and standard deviation σ = 10?
• Right-skewed distribution tail direction.
• What is the standard normal form?
• Which option is an example of ratio-level measurement?
• Which statement correctly distinguishes sampling error from non-sampling error?
• Which of the following variables is measured on a ratio scale (has a true zero)?
• Which of the following is a discrete random variable?
• Which statement correctly describes mutual exclusivity between two events A and B?
• Which statement about a CDF is true?
• In a right-skewed distribution, which statement is true?
• In the variance formula, what does S^2 denote?
• The median formula is used to
• Which statement about the range is true?
• Given Q1 = 10, Q3 = 20, IQR = 10, which value would be considered an outlier under the IQR rule?
• Which statistic is most robust to extreme outliers?
• What is a sampling distribution?
• How are quartiles typically determined in a data set?
• Which statistic is the average of squared deviations from the mean?
• What is the expected value of a fair six-sided die?
• If you have a population with variance σ^2 = 16 and you take a sample of size n = 4, what is the variance of the sample mean?
• If A and B are mutually exclusive events with P(A) = 0.4 and P(B) = 0.5, what is P(A or B)?
• In sampling without replacement, what distribution describes the number of successes in a fixed-size sample?
• If events occur at rate λ per unit time, the number of events in a fixed interval follows which distribution?
• In a box plot, which percentiles do Q1 and Q3 represent?
• If every value in a dataset occurs with the same frequency, what can be said about the mode?
• How do you compute a weighted mean of data points with weights w_i?
• Which expression correctly states the law of total probability for a partition B_i of the sample space?
• According to the empirical rule for a normal distribution, approximately what percentage lies within two standard deviations of the mean?
• Which statement correctly describes a binomial distribution?
• What is the expected value of a discrete uniform distribution on {1,2,3,4}?
• The mean is a type of
• Which statistic describes the percent of data below a threshold?
• What does N denote in a data set?
• If P(A) = 0.3, what is P(A^c) (the complement)?
• What symbol is typically used for the mean of a sample?
• A single data point in a data set is called what?
• In a joint distribution of events A and B, the marginal probability P(A) is obtained by:
• Given a data set that is sorted in ascending order, which statements correctly define Q1, Q3, and IQR?
• Which formula represents Bayes' theorem for P(A|B) in terms of P(B|A), P(A), and P(B)?
• If P(A|B) = P(A), what does this imply about A and B?
• The sample standard deviation of [2, 4, 4, 4, 5, 5, 6, 6, 7] is approximately which value?
• Which formula defines the conditional probability P(A|B)?
• Define percentile and interpret the 75th percentile.
• If the sampling size n doubles, what happens to the variance of the sample mean?
• Which statement correctly describes the marginal probability P(A) in a joint distribution with B?
• Two events A and B are independent. Which statement correctly expresses this independence?
• Define a histogram and its use.
• Using the IQR rule, which values are considered outliers?
• Which statement best describes theoretical probability?
• What is the dispersion measure defined as the difference between the largest and smallest value in a data set?
• Which statement best describes when the Poisson distribution is typically used?
• Which statement identifies the geometric distribution?
• In a left-skewed distribution, which statement is true about the relative positions of mean, median, and mode?
• How many ways can you arrange four distinct items?
• What is a random variable?
• What is a percentile?
• If P(A) = 0.7, what is P(A^c)?
• For U ∼ Uniform(a, b), what are E[U] and Var(U)?
• The mode is defined as
• What are the components of a box-and-whisker plot, and what do they represent?
• How many ways are there to choose three items from five without regard to order?
• Under what data conditions is the median preferred over the mean?
• Which condition guarantees independence of A and B?
• What does n denote in a data set?
• What symbol represents the mean of a population?
• Which statement best describes the use of a histogram?
• The interquartile range (IQR) is defined as
• What is the key difference between a bar chart and a histogram?
• For a large sample from a population with proportion p, the distribution of p-hat is approximately Normal with mean and variance given. Which is the correct pair for the mean and variance?
• What is the mean of the data set [2, 5, 7, 3, 9]?
• Which statement expresses independence between two random variables X and Y?
• Which statement correctly distinguishes a statistic from a parameter?
• Quartiles divide data into how many equal parts?
• Which statement correctly distinguishes a random sample from a convenience sample?
• Which symbol is commonly used to denote the sum of all observations?
• Which statement best describes the effect of outliers on the mean and the median?
• Which statistic is not a measure of spread?
• If A and B are independent, which statement is true?
• A geometric distribution models the number of trials until the first success. What is its mean?
• If P(A|B) = 0.6, what is P(A^c|B)?
• If data are transformed to a log-scale, how would you interpret percentiles on the log-scale relative to the original scale?
• Which of the following is the joint probability?
• Provide an example of a stratified sampling method.
• The mean of a dataset is defined as
• What is the common 3-sigma rule to identify potential outliers in a normal distribution?
• Which statement includes mean, median, and mode?
• If Q1 = 3 and Q3 = 8 for a dataset, what is the interquartile range?
• In a perfectly symmetric distribution, which statement is true about quartile distances?
• Which group of measures conveys information about the average value of a set?
• What is Pearson's first coefficient of skewness formula?
• For a Poisson distribution with rate λ, what is the expected value E[X]?
• If two events A and B are independent, how does P(A and B) relate to P(A) and P(B)?
• If X takes the values 1 and 3 with equal probability, what is Var(X)?
• Left-skewed distribution tail direction.
• Q2 corresponds to which percentile?
• What does conditional independence mean?
• In the data set [4,4,4,6,7,7,9], which statistic has the value 4?
• What is the symbol for the sum of all observations?
• If P(B) = 0.6 and P(A|B) = 0.5, what is P(A ∩ B)?
• What is P(A|B) defined as?
• How does a right-skewed distribution affect the mean relative to the median?
• What term describes a descriptive measure computed from a population?
• In a continuous distribution, what is P(X = x)?
• Which statement best describes how the variance of the sample mean relates to sample size?
• The 75th percentile is also commonly referred to as which quartile?
• Q1 observation position in a sorted data set
• If P(A|B) = 0.25 and P(B) = 0.3, what is P(A ∩ B)?
• Which formula defines the coefficient of variation for a sample?
• Bayes' theorem for two events states: P(A|B) equals what?
• Which pair of probabilities are examples of conditional probabilities?
• Which statement about histogram bin width is correct?
• Compute the weighted mean for weights w = [2, 1] and values x = [3, 5].
• To convert a z-score to a percentile, which operation is used?
• Which statement describes the mean's suitability for distributions
• What are the mean and variance of a geometric distribution with parameter p?
• Which statement correctly contrasts a population parameter with a statistic?
• Given P(B) = 0.6 and P(A|B) = 0.5, what is P(A ∩ B)?
• In the data set [1,3,3,6,8,9,9], which value is the median?
• If events A and B are disjoint with P(A) = 0.25 and P(B) = 0.40, what is P(A ∪ B)?
• For the set [4,4,4,6,7,7,9], which value is the mode?
• Which probability is derived from observed data rather than theory?
• Which expression equals Var(X) for a discrete random variable X?
• If s = 8 and n = 25, what is the standard error of the mean?
• What are the mean and variance of a binomial distribution?
• Interpret the IQR in a dataset.
• What does a confidence interval interpretation refer to?
• All possible results or outcomes of a study or experiment define which concept?
• Which level of measurement uses categories with a natural order but no meaningful zero point?
• Which statement about skewness is correct?
• What is the difference between PMF and PDF?
• Which of the following is an example of non-sampling error?
• Which statement correctly defines the p-th percentile?
• In a binomial distribution, which parameter pair defines its shape and mean?
• Using the IQR method, which of the following describes outliers?
• Which term describes a distribution where the two sides are not equal?
• If A and B are independent and P(A) = 0.4, what is P(A|B)?
• Which distribution models the number of successes in a fixed number of Bernoulli trials?
• If P(A) = 0.25, what is P(A^c)?
• Which formula expresses P(A ∪ B) in terms of P(A), P(B), and P(A ∩ B)?
• Which statement best describes the Central Limit Theorem?
• Among common measures of center, which is most robust to outliers?
• Which of the following is a continuous random variable?
• Which statement correctly characterizes interval level data?
• Which statement about a PMF is true?
• The dataset [1,2,3,4,5,6,7,8,9,10] has Q1 = 3 and Q3 = 8. What is the interquartile range (IQR)?
• What does a right-skewed histogram indicate about the data distribution?
• Which statement correctly distinguishes independence from mutual exclusivity between two events A and B?
• Which property is shared by both the mean and the median?
• Which of the following is not a property of the median?
• Kurtosis is best described as a measure of
• Q3 observation position in a sorted data set.
• Which statement about the joint probability P(A ∩ B) is true?
• The median is defined as
• Which statement most accurately describes a symmetrical distribution?
• A disease has prevalence 1%. A test with sensitivity 99% and specificity 95%. If a person tests positive, what is P(D|Pos) approximately?
• If a set of mutually exclusive outcomes covers all possibilities, their probabilities sum to what value?
• In a boxplot, whiskers extending to data points within 1.5 IQR of the quartiles indicate what about the data?
• Which statement expresses independence of A and B?
• Which expression correctly defines P(B|A)?
• Which formula expresses the probability of the union of two events?
• Which statement best distinguishes quantitative data from qualitative data?
• If A and B are disjoint with P(A) = 0.3 and P(B) = 0.25, what is P(A ∪ B)?
• How is the expected value of a discrete random variable X with PMF p(x) computed?
• A measure of dispersion is described as
• What is the general form of a 95% confidence interval for a population mean when sigma is known, and how does it change when sigma is unknown?
• Which measure of center is most robust to outliers?
• If two events A and B are independent with P(A)=0.4 and P(B)=0.5, what is P(A and B)?
• If Z is a standard normal random variable, P(-1 ≤ Z ≤ 1) is approximately which value?
• What is sampling bias and response bias? Give an example for each.
• Which statement distinguishes permutation from combination?
• What term describes a descriptive measure computed from a sample?
• What is a cumulative distribution function (CDF)?
• Which statement best describes the difference between population variance and sample variance?
• If P(B|A) = 0.5 and P(A) = 0.6, what is P(A ∩ B)?
• In the formula for the sample mean, X-bar equals which of the following?
• How does bin width affect a histogram’s representation?
• Which statement describes an event in probability?
• Which statistic equals 6 for the data set [1,3,3,6,8,9,9]?
• Compute the sample standard deviation for the data values 2, 4, 6, 8, 10.
• If P(A) equals 0.25, what is P(A^c)?
• The 3-sigma rule is applied to identify outliers in which type of distribution?
• Which statement correctly describes the standard deviation?
• Which expression defines the expected value E[X] for a discrete random variable X?
• Which symbol denotes the mean of a population variable?
• Which type of probability is derived without data?
• In a stem-and-leaf plot, what does the stem represent?
• Which statement correctly identifies a property of the mean?
• When might you apply a log transformation to data before summarizing with mean and standard deviation?
• Which statement correctly distinguishes the hypergeometric distribution from the binomial distribution?
• Which of the following best defines joint probability for two discrete variables A and B?
• In a symmetric distribution, the mean, median, and mode are what relationship?
• What statement best defines sampling bias?
• For a random sample of size n from a population with mean μ and variance σ^2, what is the approximate distribution of the sample mean as n grows large?
• In a left-skewed distribution, which order is correct?
• P(A^c) is what in terms of P(A)?
• If P(A|B) = P(A) and P(B|A) = P(B), what can we conclude?
• In n independent coin flips with probability 0.5 of heads, the number of heads follows which distribution?
• Compute the expected value E[X] for a discrete random variable X taking values 1, 2, 3 with probabilities 0.2, 0.5, 0.3.
• Which is an example of a discrete uniform distribution?
• Which term describes the likelihood of an event within the sample space?
• What is the z-score normalization (standardization) of a data point x in a dataset with mean μ and standard deviation σ?
• How do you construct a 95% confidence interval for a population mean when σ is known?
• A boxplot uses which five-number summary?
• Which statement correctly describes a property of the mode?
• Which statement about quartiles is true?
• Which statistic is the square root of the variance?
• For a Poisson distribution with λ = 3, what is P(X ≥ 3) approximately?
• Compute Var(X) for the same distribution.
• What does percentile measure?
• If X takes the values 1 and 3 with equal probability, which of the following is E[X]?
• Which expression correctly defines P(A|B)?
• Which term is defined as the average of a dataset?
• For a Binomial distribution with parameters n and p = 0.5, what are the mean and variance?
• Which statement best describes marginal probability?
• In p(A) = m/N, what does m represent?
• For a Poisson distribution with λ = 3, what is P(X = 0) approximately?
• Which property is shared by both the mean and the median?
• With P(A) = 0.3, P(B) = 0.6, and P(A ∩ B) = 0.2, what is P(A ∪ B)?
• Which symbol is commonly used to denote the variance of a sample?
• Which term best describes the group that includes the mean, median, and mode?
• Which statistic represents the middle observation when data are ordered from smallest to largest?
• What is the formula for the z-score of a value x in a distribution with mean μ and standard deviation σ?
• If two events E1 and E2 are mutually exclusive, which expression gives P(E1 ∪ E2)?
• Which statement describes a z-score?
• For a large-sample proportion, which is the correct expression for the variance of p-hat?
• Which statement correctly describes variance?
• In a scatter plot of two quantitative variables, what does a strong positive linear relationship look like?
• What is the variance of a discrete uniform distribution on {1,2,3,4,5,6}?
• What does the Law of Large Numbers state in terms of sample means?
• Which term describes measuring uncertainty and giving a precise measurement of the likelihood that an event will occur?
• In a standard deck of 52 playing cards, what is P(ace | the card drawn is a spade)?
• If X takes values 0 and 1 with probabilities 0.2 and 0.8, respectively, what is E[X]?
• If A and B are independent and P(A) = 0.4, P(B) = 0.6, what is P(A ∩ B)?
• Q2 observation position (median) in a sorted data set.
• Which term describes the central location of a dataset, including the mean, median, and mode?
• Which probability is derived from observations by collecting data?
• Which statement correctly distinguishes a population parameter from a sample statistic?