As the name indicates, the range quantifies the length of the interval in which the values of a distribution lie.
The range, usually denoted |R|, is defined as the difference between the maximum and minimum values of a distribution.
As mentioned in the definition, calculating the value of the range simply requires a single subtraction.
||R=x_{\text{max}} - x_{\text{min}}||
where |x_{\text{max}}| and |x_{\text{min}}| represent respectively the largest and the smallest values in the distribution.
Despite the simple formula, there are still a few details to consider when calculating the range.
On a spring day, the temperature outside is measured every hour. After |24| hours, the following distribution is obtained, where all the values are in Celsius (° C).
||7, 8, 10, 11, 12, 11, 10, 9, 6, 4, 3, 2, 0, -1, -3, -4, -5, -4, -3, -2, 0, 1, 2, 3||
Based on this information, determine the range of the distribution.
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Place the data in ascending order
In ascending order, it is easier to identify the maximum and minimum values.
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Apply the formula ||R = x_{\text{max}} - x_{\text{min}} = 12 - (-5) = 17||
So the range of the data is |17| °C. Despite its simplicity, the range does not provide any information about how the other data is dispersed in the distribution. For this reason, it is important to keep investigating mathematically to make an adequate analysis of the data collected.
The concept of range is also important in box-and-whisker plots. Its definition remains the same, but the interpretation becomes more interesting.