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Discrete and Continuous Random Variables

This introductory statistics lesson explains the difference between discrete and continuous random variables. It defines each type, provides examples, and helps determine if a given random variable is discrete or continuous. Students will complete worksheet 4.1.A.

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Discrete and Continuous Random Variables

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  1. Introductory Statistics Lesson 4.1 A Objective: SSBAT distinguish between discrete random variables and continuous random variables Standards: S2.5B

  2. Random Variable, x • Represents a numerical value associated with each outcome of a probability experiment. • The word Random indicates that x is determined by chance • There are 2 types of random variables: Discrete and Continuous

  3. Discrete Random Variable • A random variable that has a finite or countable number of possible outcomes • The outcomes can be listed • The outcomes can be shown as just points on a number line • Examples: • The number of students in a class • The number of patients in a doctor’s surgery • The number of calls a salesperson makes in a day

  4. Continuous Random Variable • A random variable that has an uncountable number of possible outcomes • All of the outcomes cannot be listed • The outcomes can be shown as an interval on a number line • It can be a continuous flow from one amount to another • Examples: • The time it takes to run a mile • The time spent on phone calls during a given day

  5. Ex.: Determine if each random variable is Discrete or Continuous The amount of water in a 32 ounce container  Continuous - the amount can be any number of ounces between 0 and 32

  6. Ex.: Determine if each random variable is Discrete or Continuous 2. The number of songs played by a band  Discrete - the number of songs played by a band is countable

  7. Ex.: Determine if each random variable is Discrete or Continuous 3. The length of time it takes to complete a test  Continuous – it includes all measurements of time from start to finish (can include fractional amounts) 4. The height of a tree at a nursery  Continuous – it can be any height - A tree can be 70 inches A tree can be 70.1 inches A tree can be 70.11 inches, etc

  8. Ex.: Determine if each random variable is Discrete or Continuous 5. The number of suitcases lost by an airline  Discrete 6. The number of skittles in a bag  Discrete 7. The weight of newborn babies  Continuous

  9. Discrete Random Variables are usually: When you are counting something There are only a certain amount of numbers 3. Usually include whole numbers

  10. Continuous Random Variables are usually: Amounts that can include fractions or decimals Amounts that are associated with Measuring something (weights, heights, time, etc) They include all numbers within an interval - All values between 0 and 20

  11. Complete Worksheet 4.1 A

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