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Sample Range

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The sample range is a popular and simple way to compare variability between different distributions of data. It is based on two values in a data set: the maximum, and the minimum:

sample range formula

The formula for the sample range is the largest value minus the smallest value.


The sample range is an important measure of variability for continuous variables. It acts as an estimator for the range in the population and is also the basis for finding the population standard deviation. The sample range will always be smaller than the population range unless you are fortunate enough to have the true maximum value and minimum value in your sample (in real life, this rarely happens). It can never be greater than the population range.


Disadvantages of the Sample Range

The sample range is useful for describing how spread out your data is. However, it isn’t generally considered to be an acceptable measure of spread as it will consistently underrepresent the true population range [1].

Like the sample mean, the range is sensitive to outliers. In other words, one extreme value can have a significant effect on your statistics; you should interpret the sample range with caution, taking into account any extremes in your sample data [2].

Sample Range Examples

The sample range of a variable depends on the scale of measurement. For example, the sample range for human body weight is measured in pounds and height is measured in feet/inches or centimeters. Let’s say you take a sample of people and find the shortest person is 130 cm and the tallest is 173 cm:


  • Height range = 173 cm – 130 cm = 43 cm.

For the same group of people, the lightest weight might be 100 pounds and the heaviest 201 pounds:

  • Weight range = 201 pounds – 100 pounds = 101 pounds.

References

[1] Gerstman, B. Summary Statistics.
[2] Summarizing Data: Descriptive Statistics. Introduction.

CITE THIS AS:
Stephanie Glen. "Sample Range" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/sample-range/
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