A quality characteristic of interest for a tea-bag-filling process is the weight
ID: 3252429 • Letter: A
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 should. Second, the company may be in violation of the labeling laws. For this product, the label weight on the package indicates that, on average, there are 5.5 grams of tea in a bag. If the mean 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 170 bags per minute). The data on file Teabags shown below provide the weight, in grams, of a sample of tea bags produced in one hour by a single machine
5.85
5.74
5.42
5.44
5.53
5.34
5.54
5.45
5.52
5.41
5.57
5.5
5.53
5.54
5.55
5.64
5.66
5.48
5.64
5.51
5.67
5.4
5.47
5.61
5.53
5.39
5.63
5.3
5.49
5.55
5.67
5.53
5.42
5.58
5.59
5.5
5.38
5.5
5.54
5.58
5.68
5.47
5.44
5.25
5.56
5.63
5.5
5.55
5.61
5.37
a. Compute the arithmetic mean, and median using Excel functions or Data Analysis Descriptive Statistics.
b. Compute the first quartile and third quartile using Excel function =QUARTILE.EXC
c. Compute the range, interquartile range, variance(VAR.S) standard deviation(STDEV.S) and coefficient of variation in percent format.
d. Show your understanding of statistics. You are a consultant brought in by the company. Consider the mean weight per bag. Compute how much extra tea is bagged per hour. Why should the company be concerned about the mean?
e. Consider the results of part C. Should the company be concerned about variation? Is the Coefficient Variation significant?
5.85
5.74
5.42
5.44
5.53
5.34
5.54
5.45
5.52
5.41
5.57
5.5
5.53
5.54
5.55
5.64
5.66
5.48
5.64
5.51
5.67
5.4
5.47
5.61
5.53
5.39
5.63
5.3
5.49
5.55
5.67
5.53
5.42
5.58
5.59
5.5
5.38
5.5
5.54
5.58
5.68
5.47
5.44
5.25
5.56
5.63
5.5
5.55
5.61
5.37
Explanation / Answer
a.
b.
c.
d.
The mean weight of the tea bags in the sample is 5.525 grams while the middle ranked weight is 5.3. The company should be concerned about the central tendency because that is where the majority of the weight will cluster around.The difference between the lightest and the heaviest tea bags in the sample is 0.6. 50% of the tea bags in the sample weigh between 5.45 and 5.58 grams. According to the empirical rule, about 68% of the tea bags produced will have weight that falls within 0.112 grams around 5.525 grams. The company producing the tea bags should be concerned about the variation because tea bags will not weigh exactly the same due to various factors in the production process, e.g. temperature and humidity inside the factory, differences in the density of the tea, etc. Having some idea about the amount of variation will enable the company to adjust the production process accordingly.
e.
No, Company should not be concerned about variation. The Coefficient Variation is not significant
Mean 5.525 Formula average() Median 5.53 Formula median()