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Statistics

Discrete vs Continuous Variables

Lesson

Random variables come in two flavors. Knowing which one you’ve got determines which probability tools you can use.

Discrete

Values are countable — you can list them, even if the list is infinite. Usually whole numbers from counting.

Examples: number of customers, dice rolls, defects per batch, phone calls per hour.

Continuous

Values fall on a continuous range — any real number in an interval, including all the fractions between. Usually comes from measuring (length, time, weight, temperature).

Examples: height, weight, time, temperature, voltage.

Quick test

  • “Number of ___” → almost always discrete.
  • Something measured with a tool (ruler, scale, clock) → almost always continuous.
  • If you can have 4.7 of it, it’s continuous. If only whole counts make sense, it’s discrete.

How to type your answer

Type 1 for discrete\text{discrete} and 2 for continuous\text{continuous}.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

Number of cars in a parking lot\text{Number of cars in a parking lot}

Problem 2

Height of a person\text{Height of a person}

Problem 3

Number of children in a family\text{Number of children in a family}

Problem 4

Time to run a marathon\text{Time to run a marathon}

Practice

Standard problems matching the lesson.

Problem 5

Weight of a banana\text{Weight of a banana}

Problem 6

Number of heads in 10 coin flips\text{Number of heads in 10 coin flips}

Problem 7

Distance a car travels\text{Distance a car travels}

Problem 8

Number of dice rolls until a 6 appears\text{Number of dice rolls until a 6 appears}

Problem 9

Temperature outside right now\text{Temperature outside right now}

Problem 10

Number of cards in a hand\text{Number of cards in a hand}

Problem 11

Volume of water in a bottle\text{Volume of water in a bottle}

Problem 12

Number of customers per hour at a store\text{Number of customers per hour at a store}

Problem 13

Length of a phone call (seconds)\text{Length of a phone call (seconds)}

Problem 14

Number of correct answers on a quiz\text{Number of correct answers on a quiz}

Problem 15

Speed of a car\text{Speed of a car}

Problem 16

Number of typos in a document\text{Number of typos in a document}

Problem 17

Pages printed in a day\text{Pages printed in a day}

Problem 18

Diameter of a basketball (mm)\text{Diameter of a basketball (mm)}

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

Income of a household (dollars and cents)\text{Income of a household (dollars and cents)}

Problem 20

Number of people at a concert\text{Number of people at a concert}

Problem 21

Voltage across a wire\text{Voltage across a wire}

Problem 22

Number of email replies\text{Number of email replies}

Problem 23

pH of a solution\text{pH of a solution}

Problem 24

Number of sneezes per minute\text{Number of sneezes per minute}

Problem 25

Battery life in hours\text{Battery life in hours}

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