Unit 5: Probability & Sampling Distribution of the Sample Mean

These flashcards cover key concepts from Unit 5, including definitions related to probability, random variables, distributions, and the Central Limit Theorem.

Variability

The quality of being subject to variation or changes.

Random behaviour

Unpredictable outcomes in the short-run, but regular distribution in the long-run.

Probability

A mathematical description of how likely an event is to occur, ranging from 0 to 1.

Sample space

The set of all possible outcomes of a random phenomenon.

Event

Any subset of outcomes in the sample space.

Complement

The event consisting of all outcomes not in the event A.

Probability distribution

A function that describes the likelihood of obtaining the possible values of a random variable.

Random variable

A numerical description of the outcome of a statistical experiment.

Central Limit Theorem

The theorem stating that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.

Discrete random variable

A variable that can take on a countable number of distinct values.

Continuous random variable

A variable that can take on any value within a given range or interval.

Probability of an event

Calculated by summing the probabilities of all outcomes contained in that event.

Proportion vs. Probability

A proportion is an observed value, while probability is a theoretical value.

Normal distribution

A bell-shaped distribution characterized by its mean and standard deviation.

Histogram

A graphical representation of the distribution of numerical data.

Sampling distribution of the sample mean

The distribution of values taken by the sample mean in all possible samples of the same size.

Standard deviation of the sample mean

The dispersion of the sample means around the population mean, calculated as σ/√n.