The range is one of the simplest measures of dispersion and provides a straightforward way to describe the spread or variability of a dataset. Specifically, the range represents the difference between the maximum and minimum values in a dataset.

Formula for Range:

$\text{Range}=\text{Maximum value}-\text{Minimum value}$

Range=Maximum value−Minimum value

Characteristics and Considerations:

1. Simplicity: The range is easy to calculate and understand, making it accessible for quick assessments of data variability.
2. Sensitivity to Extreme Values: The range is highly sensitive to extreme values or outliers in the dataset. A single extreme value can significantly influence the range, potentially leading to misleading interpretations of the data variability.
3. Limited Information: While the range provides a measure of the total spread of data between the minimum and maximum values, it does not provide information about the distribution of data within this range. In other words, two datasets with the same range can have very different distributions and patterns of variability.
4. Applicability: The range is applicable to datasets with ordinal, interval, or ratio level of measurement. However, its interpretation and utility may vary depending on the nature and characteristics of the data.
5. Supplemental Measures: In many cases, the range is used in conjunction with other measures of dispersion, such as the interquartile range, variance, or standard deviation, to provide a more comprehensive and nuanced understanding of data variability.

Example:

Consider the following dataset representing the daily temperatures (in degrees Celsius) for a week:

$18,20,22,25,19,28,17$

18,20,22,25,19,28,17

To calculate the range:

1. Identify the maximum and minimum values:
   • Maximum value = 28
   • Minimum value = 17
2. Calculate the range:
   
   $\text{Range}=28-17=11$

    

   Range=28−17=11

The range of the daily temperatures for the week is 11 degrees Celsius, indicating the total spread or variability of temperatures observed over the week.

The range provides a basic measure of dispersion that captures the total spread of data between the minimum and maximum values. While it offers simplicity and ease of calculation, the range has limitations, particularly its sensitivity to extreme values and the lack of information about the distribution of data within the range. As such, the range is often used in conjunction with other measures of dispersion to provide a more comprehensive and nuanced assessment of data variability and distribution.