Topics in a Probability and Statistics Course

To 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 Distribution	The 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 Test	A statistical test for evaluating hypotheses involving enumerated data.
Conditional Probability	The probability of an event, assuming that some other event has already occurred.
Confidence Interval	An 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.
Histogram	The 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 Events	A 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 one of a triangle's vertices to the midpoint of the opposite side.
Moment	A 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."
Outlier	A point in a sample that has a substantially different value from the rest.
Paired t-Test	A 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.
Sample	From 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 Deviation	A 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.
Variance	A measure of the expected deviation from the mean. The square root of the variance is the standard deviation.
z-Score	The difference from the mean divided by the standard deviation. Also called the "standard score." MathWorld