Real Limits, Apparent Limits, and Frequency Distributions

 

• Recall that a continuous variable has an infinite number of possible values. It can be represented by a number line that is continuous and has an infinite number of points. However, when we measure a continuous variable we have only a finite measurement process, resulting in numbers that have a finite precision.

• If our measurements of a continuous variable are all numbers that are all in whole integer units, our precision of measurement is 1 unit. In this measurement situation, an observed value of 8 would be obtained when the "real value" is 7.8 or 8.21, or any other value between 7.5 and 8.5. Thus, the observed value of 8 actually represents a range of "real values" from 7.5 to 8.5. These values are called the "real limits".

  

• The concept of "real limits" also applies to class intervals. In the table at the right the interval denoted as "60-64" actually has "real limits" of 59.5-64.5. The values denoting the interval as 60-64 are called the "apparent limits".

 

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