The mean (or average) of a set of data is calculated by summing all the data points and dividing by the number of data points: \[ \text{Mean} = \frac{\sum X_i}{n} \] where \( X_i \) represents each data point and \( n \) is the number of data points.

The median is the middle value of a data set when the numbers are arranged in ascending order. If the number of data points is odd, the median is the middle value. If the number of data points is even, the median is the average of the two middle numbers.

The standard deviation measures the spread of data points around the mean. It is calculated as: \[ \sigma = \sqrt{\frac{\sum (X_i - \mu)^2}{n}} \] where \( X_i \) represents each data point, \( \mu \) is the mean, and \( n \) is the number of data points.

The p-value is the probability of observing a test statistic as extreme as, or more extreme than, the value observed under the assumption that the null hypothesis is true. A small p-value (typically less than 0.05) indicates strong evidence against the null hypothesis.

A confidence interval gives a range of values within which we can be confident that the population parameter lies. It is typically constructed as: \[ \text{Confidence Interval} = \bar{x} \pm Z \left(\frac{\sigma}{\sqrt{n}}\right) \] where \( \bar{x} \) is the sample mean, \( Z \) is the z-score corresponding to the confidence level, \( \sigma \) is the population standard deviation, and \( n \) is the sample size.

Correlation refers to a statistical relationship between two variables, where changes in one variable are associated with changes in the other. Causation indicates that one variable directly affects another. While correlation can suggest a possible relationship, it does not prove causation.

The probability of an event \( A \) is calculated as: \[ P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \] This assumes that all outcomes are equally likely.

The central limit theorem states that, given a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the original distribution of the population. This is crucial for making inferences about population parameters.

A normal distribution is a continuous probability distribution that is symmetric around the mean, with the data spread in a bell-shaped curve. Its key properties include: - The mean, median, and mode are equal. - Approximately 68% of the data lies within one standard deviation of the mean, 95% within two, and 99.7% within three (68-95-99.7 rule).

A population refers to the entire set of individuals or items that are of interest in a statistical study, while a sample is a subset of the population that is actually observed or analyzed. Inferences about the population are often made based on data from the sample.