Statistics: Discrete Data

Discrete Data

• 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.

Discrete Random Variable

• 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

• 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.

Continuous Random Variable

• 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).

Error Probable

• 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.