The mean is among the most fundamental tools in statistics for describing the central behavior of a data distribution.

The arithmetic mean is the most common and intuitive form of average. As a special case within the broader family of power means it expresses the representative value of a data set by dividing the...

The geometric mean belongs to the family of power means. Unlike the simple arithmetic mean, it is based on the product of the elements rather than their sum, making it especially useful for measuring...

The harmonic mean belongs to the broader family of power means and plays a distinctive role whenever the data being analyzed combine reciprocally rather than additively.

The quadratic mean, also called the root mean square, belongs to the general family of power means. It is obtained by taking the square root of the arithmetic mean of the squared values in a dataset.

The median is a key measure of central tendency used to describe the typical value within a dataset. While the mean expresses the numerical balance of all values, the median focuses instead on...

One of the key principles in statistics is that the mean alone cannot fully describe a dataset. What truly matters is understanding how the individual observations are spread around the mean, that...

A discrete random variable is a function that assigns a real number to each element of a discrete sample space.

A continuous random variable is a function that assigns a real number to each element of a continuous sample space.

The mean represents a fundamental statistical measure that characterizes the central tendency of a dataset.

In descriptive statistics, the variance expresses how much a set of values differs, on average, from its mean.

The binomial distribution is a discrete probability distribution that models the number of successes in a sequence of independent experiments, each one following a Bernoulli distribution with the...

The hypergeometric distribution is a discrete probability distribution that describes the number of successes drawn from a finite population without replacement.

The geometric distribution describes the number of independent trials required to observe the first success in a repeated experiment.

The Poisson distribution is a discrete probability distribution that describes how many times a specific event may occur within a fixed period of time or space.

The uniform distribution is one of the simplest continuous distributions to describe. It models a random variable that can take any value within a specified interval, assigning the same probability...

The beta distribution is a continuous probability distribution defined over the open interval ( 0 , 1 ).

The normal distribution, also known as the Gaussian distribution, is one of the most important continuous probability distributions in both probability and statistics.

A generic normal distribution \mathcal{N} ( x ; \mu , \sigma ) can always be transformed into its standardized form N ( x ; 0 , 1

The gamma distribution is a continuous probability distribution defined on the positive half-line. It is used to model waiting times, event durations, and phenomena where independent contributions...

The chi-square distribution is a continuous probability distribution that arises from analyzing how the sum of squared observations behaves when those observations follow a standard normal...

In statistical inference, when the goal is to draw conclusions about the mean of a normally distributed population but the variance is unknown and must be estimated from the sample, the standard...

The exponential distribution characterizes the time elapsed between random, independent events occurring at a constant average rate.

A sampling distribution represents the distribution of a statistic obtained from all possible samples of a given size drawn from a population.

Bayes’ Theorem is a fundamental result in probability theory that describes how to compute the conditional probability of a hypothesis given observed evidence.

When we rely on a sample to learn something about an unknown population parameter, say the mean \mu, a natural first step is to use a point estimator.