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The best example I can think of concerning discrete data versus continuous data comes from word problems in Basic Algebra (Algebra I). When solving a perimeter problem, the answers do NOT have to come out even. When you solve for x, where x is the width or length of a rectangle, you COULD have a fraction for the answer. It doesn't have to come out to a whole number. You can have a half a foot, or a third of a foot, or any fractional value of a foot or meter or inch or centimeter. This is an example of a continuous variable.
However, in a coin problem it's different. The solution MUST come out to a whole number, since you can't have a fractional or decimal part of a coin. You can't have a half a nickel or a third of a dime or one sixth of a quarter. This would be an example of a discrete variable. In other words discrete data refers to data that is measured in specific numbers that cannot be measured over an entire interval of numbers. For continuous data, it CAN represent any values within an interval.
Consider the measurement of the heights of people: Continuous or discrete? The answer is usually continuous, since the heights of people is usually measured on a continous scale, not in specific units. However, if you set up intervals of heights of people, and placed the actual heights of people measured in categories, that would be discrete data. If you measured the heights of people and rounded off to the nearest foot, or centimeter, or inch, this would be discrete data.
Consider the problem of finding consecutive integers: Continuous or discrete? The answer is discrete, since the answers must come out even.
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