4.2:
Range
The range is a measure of variation, defined as the difference between the maximum and minimum values.
Consider a dataset on the weights of different breeds of dogs. The difference between the weight of the heaviest breed of dog, the English Mastiff, and that of the smallest dog breed, the Chihuahua, gives the range of the dataset.
Here, the range value of 101 kg denotes the weight variation among different breeds of dogs. The average weight of any dog breed, in this example, will fall within this dispersion or spread.
The range relies only on the maximum and minimum, or extreme values, unlike other measures of variation. Therefore, the range has limited use because of its sensitivity to outliers and lack of robustness.
Since the range is easier to compute, it is often used to prepare control charts for manufacturing and weather forecasting applications.
4.2:
Range
The range is one of the measures of variation. It can be defined as the difference between a dataset's highest and lowest values. For example, in the study of seven 16-ounce soda cans, the filled volume of soda was measured, thus producing the following amount (in ounces) of soda:
15.9; 16.1; 15.2; 14.8; 15.8; 15.9; 16.0; 15.5
Measurements of the amount of soda in a 16-ounce can vary since different subjects record these measurements or since the exact amount – 16 ounces of liquid, was not poured into the containers. Manufacturers regularly perform tests to determine if the amount of soda in the can falls within the desired range. For the given dataset, the range is calculated as the difference between the largest and smallest values: 16.1 − 14.8 = 1.3.
The range relies heavily on the extreme values, that is, the maximum and minimum values. Hence, it is highly susceptible to outliers and lacks robustness in measurement. However, it is relatively easy to compute; therefore, it is used widely in statistical process control in manufacturing, as shown in the above example.