An essential property of concern for a thyme bottle-filling machine is the weight of the thyme in the individual bottles. If the bottles are under filled, two problems arise. First, customers may not have enough thyme for their spice needs. 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 1.62 ounces of thyme in a bottle. If the average amount of thyme in a bottle exceeds the label weight, the company is giving away product. Getting an exact amount of thyme in a bottle is problematic because of variation in the temperature and humidity inside the factory, differences in the density of the thyme, and the extremely fast filling operation of the machine (approximately 300 bottles a minute). The following table provides the weight in ounces of a sample of 50 bottles produced in one hour by a single machine:
2.63 1.96 1.57 1.71 1.69
1.69 1.62 .89 1.79 1.78
1.54 1.47 1.96 1.61 1.63 1.59 1.76 1.64 1.39 1.59
1.62 1.66 1.28 1.77 1.42 1.49 1.67 1.46 1.65 1.62
1.87 1.73 1.54 1.88 1.38 .98 1.63 1.69 1.37 1.52
1.78 1.89 1.62 1.63 1.43 1.52 1.43 1.89 1.37 1.76
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 thyme bottles be concerned about the central tendency?
e. Interpret the measures of variation within the context of this problem. Why should the company producing the thyme bottles be concerned about variation?