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 company 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 3.40 grams of tea in a bag. If the average amount of tea in a bag exceeds the label weight, the company is giving away product. Getting an exact amount of tea in a bag is problematic because of variation in the temperature and humidity inside the factory, differences in the density of the tea, and the extremely fast filling operation of the machine (approximately 215 bags a minute). The following table provides the weight in grams of a sample of 50 bags produced in one hour by a single machine:

2.95 3.70 3.42 3.40 3.53 2.54 3.54 3.45 3.52 3.81
3.57 3.40 3.83 2.54 3.55 2.62 3.66 3.46 2.64 3.51
3.67 3.40 3.47 3.61 2.53 3.32 2.67 3.29 3.49 3.55
3.77 3.57 3.42 3.58 3.68 3.50 3.32 3.50 3.53 2.58
3.61 3.45 3.44 3.25 3.56 3.63 3.50 2.57 3.67 3.36

a. Compute the arithmetic mean and median.
b. Compute the first quartile and third quartile.
c. Compute the range, interquartile range, variance, standard deviation, and coefficient of variation.
d. Interpret the measures of central tendency within the context of this problem. Why should the company producing the tea bags be concerned about the central tendency?
e. Interpret the measures of variation within the context of this problem. Why should the company producing the tea bags be concerned about variation?