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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 Arithmetic mean is a synonym for average, i.e., the sum of all values in a list divided by the number of values present.
Binomial Distribution The binomial distribution is a discrete probability distribution of obtaining exactly n successes out of N trials.
Box-and-Whisker Plot A box-and-whiskers plot is a histogram-like method of displaying data.
Central Limit Theorem The central limit theorem states 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 The chi-squared test is a statistical test for evaluating hypotheses involving enumerated data.
Conditional Probability Conditional probability is the probability of an event, assuming that some other event has already occurred.
Confidence Interval A confidence interval is an interval in which a measurement or trial falls that corresponds to a given probability.
Correlation Coefficient The correlation coefficient measure of how closely a best-fit curve matches the given data.
Covariance The covariance of a set of variables is a measure of the strength of their correlation.
Erf The error function, commonly denoted erf, is the function involved in integrating the normal distribution.
Histogram A histogram is a visual grouping of data into bins, plotting the number of members in each bin against the bin number.
Hypothesis (1) In the mathematical and physical sciences, the term hypothesis is often used as a rough synonym for conjecture . (2) In statistics, a hypothesis is a statement that can be tested. (3) In logic, a hypothesis is the first part of a logical implication.
Independent Events Events are said to be independent if the occurrence of one does not influence the probability that the others will occur.
Law of Large Numbers The law of large number is one of several mathematical 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 In statistics, a mean is quantity corresponding to one of possibly several different definitions of the "average" of a set of values, such as the arithmetic, geometric, or harmonic mean. In the absence of additional context, the term "mean" most commnly refers to the arithmetic mean (i.e., the average).
Median (1) In statistics, the median is an order statistic that gives the "middle" value of a sample. (2) In geometry, the median of a triangle is a line segment from one of its vertices to the midpoint of the opposite side.
Mode The mode of a set of observations is the most commonly occurring value. A distribution with a single mode is said to be unimodal. A distribution with more than one mode is said to be bimodal, trimodal, etc., or in general, multimodal.
Moment In statistics, a moment is a measure of the expected deviation from the mean. The most important example of a moment is the variance.
Normal Distribution The normal distribution is a probability distribution associated with many sets of real-world data. Due to the shape of this distribution, it is also famously called the "bell curve."
Outlier In statistics, an outlier is a point in a sample that has a substantially different value from the rest.
Paired t-Test The paired t-test is a statistical test that determines whether the means of two sample sets differ significantly.
Poisson Distribution The Poisson distribution is the statistical distribution giving the probability of obtaining exactly n successes in N trials for Poisson processes such as radioactive decay and lotteries.
Probability Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions.
Problem A problem is an exercise whose solution is desired. Mathematical problems may therefore range from simple puzzles to examination and contest problems to propositions whose proofs require insightful analysis and high-level knowledge.
Sample In mathematics, a sample of a population is a subset that is obtained to investigate the parent population's properties.
Scatter Diagram A scatter diagram is 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 The standard deviation is a statistic defined as the square root of the variance that measures how spread out a set of data is.
Statistical Test A statistical test is a test used to determine the statistical significance of an observation.
Statistics Statistics is 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 uniform distribution is a probability distribution that has constant probability.
Variance In statistics, variance is the measure of the expected deviation from the mean. The square root of the variance is the standard deviation.
z-Score A z-score, also called a "standard score," is the difference from the mean divided by the standard deviation.