{
  "deck_name": "Statistics Essentials",
  "cards": [
    { "question": "What is the difference between a population and a sample?", "answer": "A population is the full group of interest; a sample is a subset observed from that group." },
    { "question": "What does a statistic describe?", "answer": "A numerical summary calculated from sample data; a parameter describes a population." },
    { "question": "What is the arithmetic mean of a data set?", "answer": "The sum of the observations divided by the number of observations." },
    { "question": "How is the median found?", "answer": "Order the observations and take the middle value, or the mean of the two middle values when there is an even count." },
    { "question": "What is the mode of a data set?", "answer": "The value or values that occur most often; a data set can have more than one mode or none." },
    { "question": "When can the median be a more useful measure of center than the mean?", "answer": "When a distribution is skewed or contains influential outliers, because the median is less affected by extreme values." },
    { "question": "What does the range measure?", "answer": "The maximum value minus the minimum value in the data set." },
    { "question": "What does the interquartile range (IQR) measure?", "answer": "The spread of the middle half of ordered data: the third quartile minus the first quartile." },
    { "question": "What does variance summarize?", "answer": "The average squared deviation from the mean, using a population or sample formula as appropriate." },
    { "question": "How does the sample variance denominator differ from the population variance denominator?", "answer": "Sample variance commonly divides the squared deviations by n − 1; population variance divides by N." },
    { "question": "How is standard deviation related to variance?", "answer": "Standard deviation is the nonnegative square root of variance, so it is expressed in the original data units." },
    { "question": "What does a z-score measure?", "answer": "How many standard deviations an observation is above or below its distribution's mean: z = (x − μ) / σ." },
    { "question": "What is the probability of an event's complement?", "answer": "For an event A, P(not A) = 1 − P(A)." },
    { "question": "When can the addition rule simplify the probability of A or B?", "answer": "For mutually exclusive events, P(A or B) = P(A) + P(B)." },
    { "question": "How does independence affect the probability of two events occurring together?", "answer": "If A and B are independent, P(A and B) = P(A) × P(B)." },
    { "question": "What does conditional probability P(A | B) mean?", "answer": "The probability that A occurs given that B is known to have occurred, when P(B) is greater than zero." },
    { "question": "What is the expected value of a discrete random variable?", "answer": "The sum of each possible value multiplied by its probability: E(X) = Σ xP(x)." },
    { "question": "What parameters determine a normal distribution?", "answer": "Its mean μ determines its center and its standard deviation σ determines its spread." },
    { "question": "What are the mean and standard deviation of the standard normal distribution?", "answer": "Its mean is 0 and its standard deviation is 1." },
    { "question": "What does the empirical 68–95–99.7 rule describe?", "answer": "For an approximately normal distribution, about 68%, 95%, and 99.7% of values lie within 1, 2, and 3 standard deviations of the mean." }
  ]
}