Final answer:
The expected value or mean is a statistical term representing the long-term average of an experiment's outcomes when repeated many times. It can be calculated using the formula E(X) = μ = Σ xP(x) for a discrete random variable. Variance and standard deviation are related concepts that describe the data's spread around the mean.
Step-by-step explanation:
The expected value, or mean, is the long-term average that results from a statistical experiment when repeated many times. The expected value for a discrete random variable (RV) can be calculated using the sum of the products of each possible value of the random variable and its probability, represented by the formula E(X) = μ = Σ xP(x). For example, when calculating the expected value of the number of heads in tossing three fair coins, if this experiment is repeated many times, the expected value represents the average number of heads you would obtain per set of three tosses.
Variance and standard deviation are measures related to expected value, but they characterize the spread of a set of numbers. Variance is the square of the standard deviation and is a measure of how far a set of numbers is spread out from their mean. Standard deviation, symbolized by the Greek letter sigma (σ), is the square root of the variance and provides an indication of the uncertainty or precision of the expected value.
Meanwhile, the median is the middle number in a sorted list of numbers, and the mode is the number that appears most frequently in a data set. These are also measures of central tendency, but unlike expected value, they are not influenced by the extremity of values in a data set.