3.4. Discrete and Continuous Measurements

The two types of measurements we are concerned about when applying staticists to engineering problems are discrete measurements and continous measurements.

Discrete Measurements

All data that are the result of counting are called discrete measurements. These data take on only certain numerical values. If you count the number of phone calls you receive for each day of the week, you might get values such as zero, one, two, or three. Discrete measurements can also include simple probabilities such as the flip of a coin or the toss of a die.

For example: Role a six sided die.

• 6 discrete results 1,2,3,4,5, or 6

• equal probability of occurrence of 1 in 6

Countinous Measurements

Measured data may include fractions, decimals, or irrational numbers. These types of measurements are called continuous measurements. Continuous measurements are often the results of measurements like length, mass, or time. A record of the time or duration in minutes for all the phone calls that you make in a week, with numbers like 2.4 min, 7.5 min, or 11.0 min, would be continuous measurements.

For example: The probability of a person’s age is not a discrete value. We can cut time into infinitesimally small increments.

Worked Example

GIVEN:

You go to the supermarket and purchase three cans of soup (19 ounces tomato bisque, 14.1 ounces lentil, and 19 ounces Italian wedding soup), two packages of nuts (walnuts and peanuts), four different kinds of vegetables (broccoli, cauliflower, spinach, and carrots), and two desserts (16 ounces pistachio ice cream and 32 ounces chocolate chip cookies).

FIND:

Name data sets that are discrete measurements, and continuous measurements.

SOLUTION:

The three cans of soup, two packages of nuts, four kinds of vegetables and two desserts are discrete measurements because you count them.

The weights of the soups (19 ounces, 14.1 ounces, 19 ounces) are continuous measurements because you measure weights as precisely as possible.