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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