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A bell-shaped probability distribution that is symmetrical about the mean. Example: Heights of people are often normally distributed.

The set of all possible outcomes of a random experiment. Example: For a six-sided die, the sample space is {1, 2, 3, 4, 5, 6}.

A measure of how spread out numbers are from the mean. Example: In a set {2, 4, 4, 4, 5, 5, 7, 9}, the standard deviation is approximately 2.

A statistical method for estimating the relationships among variables. Example: Predicting height based on age and gender using past data.

A statistical test used to determine whether there is a significant association between categorical variables. Example: Determining if there is a relationship between gender and voting preference.

A hypothesis that there is no effect or no difference, and it is the hypothesis that researchers typically try to disprove. Example: The null hypothesis may be that a new drug has no effect on a disease.

A range of values that is likely to contain a population parameter with a certain level of confidence. Example: A 95% confidence interval for the mean might be (45, 55).

Two events where the occurrence of one event does affect the likelihood of the other. Example: Drawing two cards from a deck without replacement.

The probability distribution of the number of successes in a fixed number of independent yes/no experiments, each of which yields success with a given probability. Example: The distribution of flipping a coin 10 times and counting the number of heads.

The hypothesis that there is an effect or a difference. Example: Believing that a new drug does have an effect on a disease.

Two events that have no influence on the likelihood of each other occurring. Example: Flipping a coin and rolling a die are independent events.

The middle value in a list of numbers. Example: For the set {1, 3, 3, 6, 7, 8, 9}, the median is 6.

The probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct. Example: A p-value of 0.05 or less is often considered statistically significant.

The likelihood that a result or relationship is caused by something other than mere random chance. Example: A study finding that a drug is effective with a p-value of 0.03 may be considered statistically significant.

A method of making statistical decisions using experimental data. Hypothesis testing is used to determine whether there is enough evidence in a sample of data to infer that a certain condition holds for the entire population. Example: Determining whether a new drug is effective, based on sample trial data.

The theory that the sum of a large number of independent and identically distributed random variables tends towards a normal distribution, regardless of the original distribution of the variables. Example: Average of die rolls.

The value that appears most often in a set of data. Example: In the set {1, 2, 4, 4, 7}, the mode is 4.

The error of rejecting a true null hypothesis (false positive). Example: Convicting an innocent person.

The anticipated value for an investment in the future. In probability, it is calculated as the sum of all possible values each multiplied by the probability of its occurrence. Example: The expected value of rolling a six-sided die is $3.5$.

A principle that states as a sample size grows, its mean gets closer to the average of the whole population. Example: Flipping a coin many times will result in an average close to 0.5 heads.

The arithmetic average of a set of values, calculated by adding them all up and dividing by the number of values. Example: For the set {2, 3, 4}, the mean is (2+3+4)/3 = 3.

A probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space. Example: The number of emails one receives in an hour.

An arrangement of objects in a specific order. The formula for the number of permutations of n objects taken r at a time is $P(n, r) = \frac{n!}{(n-r)!}$. Example: The number of ways to arrange 3 books on a shelf from a set of 5 is $P(5, 3) = \frac{5!}{(5-3)!} = 60$.

A formula that describes how to update the probabilities of hypotheses when given evidence. In its simplest form, it can be written as $P(A|B) = \frac{P(B|A)P(A)}{P(B)}$. Example: Updating the probability of having a disease given a positive test result.

A measure of the likelihood that an event will occur, expressed as a number between 0 and 1. Example: The probability of flipping a head on a fair coin is 0.5.

The number of standard deviations a data point is from the mean. Example: A z-score of 2 means the data point is 2 standard deviations above the mean.

The error of not rejecting a false null hypothesis (false negative). Example: Failing to detect a disease in a person who actually has the disease.

A selection of objects without regard to the order. The formula for the number of combinations of n objects taken r at a time is $C(n, r) = \frac{n!}{r!(n-r)!}$. Example: The number of ways to choose 3 books from a set of 5 is $C(5, 3) = \frac{5!}{3!(5-3)!} = 10$.

The probability distribution of a given statistic based on a random sample. Example: The distribution of sample means for samples of a given size drawn from a population.

A variable that takes on different numerical values, each with a certain probability. Example: The sum on two dice when rolled.

Events that cannot occur at the same time. Example: Rolling a 3 and a 5 on a single die at the same time.

The average of the squared differences from the mean. Example: For the set {2, 4, 4, 4, 5, 5, 7, 9}, the variance is approximately 4.

A measure that indicates the extent to which two variables are related. Example: A correlation coefficient of 0.9 suggests a strong positive relationship between two variables.

A function that describes the likelihood of obtaining the possible values that a random variable can assume. Example: The probability distribution of a fair six-sided die roll is each number 1-6 with a probability of 1/6.