Notation
A set intersection of two sets, A and B, denoted by A ∩ B, is a subset of A or B that contains all elements that are in both A and B. In other words, A ∩ B := { x : x in A and x in B}.
A set union of two sets, A and B, denoted by A ∪ B, is a set that contains precisely the elements that are in A or in B. In other words, A ∪ B := { x : x in A or x in B}.
A set difference of two sets, A and B, denoted by A – B or A\B, is a subset of A that contains all elements in A that are not in B. In other words, A – B := { x : x in A and x not in B}.
The summation symbol, ∑, represents the sum of all members over the set, for example:
Definitions and terms
- Population: A set of similar data or items subject to analysis.
- Sample: A subset of the population.
- Arithmetic mean (average) of a set: The sum of all the values in the set divided by the size of the set.
- Median: The middle value in an ordered set, for example, the median of the set {x1, …, x2k+1}, where x1 <…< x2k+1 is the value xk+1.
- Random variable: A function from a set of possible outcomes (for example, heads or tails) to a set of values (for example, 0 for heads and 1 for tails).
- Expectation: An expectation of a random variable is the limit of the average values of the increasing sets of the values given by the random variable.
- Variance: Measures the dispersion of the population from its mean. Mathematically, the variance of a random variable, X, is the expected value of the square of the difference between the random variable and the mean μ of X, that is, .
- Standard deviation: The deviation in the random variable, X, is the square root of the variation in the X variable, that is, .
- Correlation: The measure of the dependency between the random variables. Mathematically, for the random variables X and Y, the correlation is defined as .
- Causation: A dependence relation explaining the occurrence of one phenomenon through the occurrence of another phenomenon. Causation implies correlation, but not vice versa!
- Slope: The a variable in the linear equation y=a*x+b.
- Intercept: The b variable in the linear equation y=a*x+b.