Statistics: Discrete Data

Study Notes

Discrete data is not continuous and has a limited number of possible values.
Examples of discrete data: number of students in a class, number of workers in a company, number of parts damaged during transportation, shoe sizes, number of languages an individual speaks, and number of test questions answered correctly.
Discrete data can be graphically displayed by bar graphs, stem-and-leaf plots, and pie charts.

A discrete random variable X has a finite or countable infinite number of possible values.
The probability of X having a specific value is non-zero, and the sum of probabilities is equal to 1.
Theorems on expected value:
- If c is a constant, then E(cX) = cE(X)
- If X and Y are independent random variables, then E(X+Y) = E(X) + E(Y) and E(XY) = E(X)E(Y)

Continuous data is information that can be measured on a scale or continuum and can have almost any numeric value.
Examples of continuous data: amount of time required to complete a project, height of children, amount of time it takes to sell shoes, amount of rain that falls in a storm, weight of a truck, speed of cars, and time to wake up.
Continuous data can be graphically displayed by histograms and line graphs.
Continuous data is measurable and has an infinite number of possible values within an interval.

A continuous random variable X can assume any value in a given interval (bounded or unbounded).
Exponential distribution: a random variable X is exponentially distributed with parameter λ > 0 if its probability distribution function is f(x) = λe^(-λx).

Circular Error Probable (CEP) is the radius of the circle about the true mean point, which includes 50% of the hits.
Range Error Probable (REP) is a one-dimensional measure of dispersion and is used to measure range precision in firing.
The CEP is generally used to describe weapon delivery accuracy.