AP Statistics Flashcards: Mean and Standard Deviation of Random Variables
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 11 cards to help you master important concepts.
What is a parameter?
A parameter is a numerical value that measures a characteristic of a population or a probability distribution.
Card 1 of 11
All Flashcards (11)
What is a parameter?
A parameter is a numerical value that measures a characteristic of a population or a probability distribution.
What does the mean, or expected value, of a discrete random variable represent?
The mean represents the long-run average value of the random variable if the random process were repeated many times.
What must be calculated before you can find the standard deviation of a discrete random variable?
The mean (expected value) of the discrete random variable must be calculated first, as the standard deviation is based on deviations from the mean.
How is the standard deviation of a discrete random variable X calculated?
The standard deviation is the square root of the sum of each squared deviation from the mean multiplied by its corresponding probability.
What two key components must be included when interpreting the parameters of a discrete random variable?
Any interpretation of a parameter for a discrete random variable must be in the context of the problem and include appropriate units.
How is the mean (or expected value) of a discrete random variable X calculated?
The mean is calculated by finding the sum of each possible value of the random variable multiplied by its corresponding probability.
Define the expected value of a discrete random variable X.
The expected value of X, another name for its mean, is the sum of the product of each possible value and its probability.
What does the standard deviation of a discrete random variable measure?
The standard deviation measures the typical or average distance of the outcomes of the random variable from the mean.
A discrete random variable X represents the number of defective items in a batch. If the mean is 2.5 items, how would you interpret this value?
If we were to examine many batches, the average number of defective items per batch would be about 2.5.
What are the two primary skills related to parameters for a discrete random variable?
The two primary skills are to calculate the parameters (like mean and standard deviation) and to interpret them in context.
A random variable has a standard deviation of 1.2 points. How would you interpret this value in context?
The value of the random variable typically varies from the mean by about 1.2 points.