Question: A quality characteristic of interest for a tea-bag filling process is the weight of the tea in the individual bags. If the bags are under filled, two problems arise.  First, customers may not be able to brew the tea to be as strong as they wish.  Second, the firm may be in violation of the truth-in-labeling laws.  In this example, the label weight on the package indicates that, on average, there are 5.3 grams of tea in a bag.  If the average amount of tea in a bag exceeds the label weight, the firm is giving away product.  Getting an exact amount of tea in a bag is problematic because of variation in the temperature & humidity inside the factory, differences in the density of the tea, & the extremely fast filling operation of the machine (approximately 170 bags a minute).  The following table provides the weight in grams of a sample of fifty bags produced in one hour by a single machine:

Find the measures of variation within the context of this problem. Why should the firm producing the tea bags be concerned about variation?