Topics in a Probability and Statistics CourseTo learn more about a topic listed below, click the topic name to go to the corresponding MathWorld classroom page.

Arithmetic Mean A synonym for average.

Binomial DistributionThe discrete probability distribution of obtaining exactly n successes out of N trials.

Box-and-Whisker Plot A histogram-like method of displaying data.

Central Limit Theorem

The theorem that any set of variates with a distribution having a finite mean and variance tends to the normal distribution. This allows statisticians to approximate sets of data with unknown distributions as being normal.

Chi-Squared TestA statistical test for evaluating hypotheses involving enumerated data.

Conditional ProbabilityThe probability of an event, assuming that some other event has already occurred.

Confidence IntervalAn interval in which a measurement or trial falls that corresponds to a given probability

Correlation Coefficient A measure of how closely a best-fit curve matches the given data.

Covariance A measure of how strongly correlated

a set of variables is.

Erf The error function involved in integrating the normal distribution.

HistogramThe grouping of data into bins, plotting the number of members in each bin against the bin number.

Hypothesis

(1) In statistics, a statement that can be tested. (2) A rough synonym of conjecture. (3) In logic, the first part of an implication.

Independent EventsA property of two events A and B if their probabilities satisfy P(AB) = P(A) P(B).

Law of Large Numbers

One of several theorems expressing the idea that as the number of trials of a random process increases, the percentage difference between the expected and actual result values goes to zero.

Least Squares Fitting

A mathematical procedure for finding the best-fitting curve to a given set of points by minimizing the sum of the curve's squared offsets from the data.

Mean

(1) A quantity corresponding to one of possibly several different definitions of the "average" of a set of values. Examples include the arithmetic mean and the geometric mean. (2) The arithmetic mean (also called the average).

Median (1) The statistical median, which is an order statistic that gives the "middle" value of a sample. (2) A triangle median, which is a line segment from

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one of a triangle's vertices to the midpoint of the opposite side.

MomentA measure of the expected deviation from the mean. The most important example of a moment is the variance.

Normal Distribution

The distribution associated with most sets of real-world data. Due to the shape of this distribution, it is also famously called the "bell curve."

OutlierA point in a sample that has a substantially different value from the rest.

Paired t-TestA statistical test that determines whether the means of two sample sets differ significantly.

Poisson Distribution

The distribution giving the probability of obtaining exactly n successes in N trials for Poisson processes such as radioactive decay and lotteries.

Probability

The branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.

SampleFrom a population, a subset that is obtained to investigate the parent population's properties.

Scatter Diagram

A graphic which shows data where one variable has been plotted against a second variable. Scatter diagrams are used when investigating correlation between two variables.

Standard DeviationA statistic that measures how spread out a set of data is. It is defined as the square root of the variance.

Statistical Test A test used to determine the statistical significance of an observation.

Statistics

The mathematical study of the likelihood and probability of events occurring, based on known information and inferred by taking a limited number of samples.

Uniform Distribution A distribution that has constant probability.

VarianceA measure of the expected deviation from the mean. The square root of the variance is the standard deviation.

z-ScoreThe difference from the mean divided by the standard deviation. Also called the "standard score."

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