A quality characteristic of interest for a tea-bag-filling process is the weight
ID: 3171415 • 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 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 5.5 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 170 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: 5.85 5.74 5.42 5.4 5.53 5.34 5.54 5.45 5.52 5.41 5.57 5.5 5.53 5.54 5.55 5.68 5.66 5.48 5.64 5.51 5.67 5.4 5.47 5.61 5.53 5.32 5.7 5.3 5.49 5.55 5.67 5.56 5.42 5.58 5.59 5.5 5.39 5.5 5.53 5.58 5.68 5.45 5.44 5.25 5.56 5.63 5.5 5.57 5.67 5.36
Compute the arithmetic mean and median. Compute the first quartile and third quartile. Compute the range, interquartile range, variance, standard deviation, and coefficient of variation.
Parts d and e are your chance to show your understanding. You are a consultant brought in by the company and given the sample.
What are your recommendations to the company, based on your reading for this week? 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?
Interpret the measures of variation within the context of this problem. Why should the company producing the tea bags be concerned about variation?
Explanation / Answer
Answer: First we sort the data in ascending order.
5.25 5.30 5.32 5.34 5.36 5.39 5.40 5.40 5.41 5.42 5.42 5.44 5.45 5.45 5.47
5.48 5.49 5.50 5.50 5.50 5.50 5.51 5.52 5.53 5.53 5.53 5.53 5.54 5.54 5.55
5.55 5.56 5.56 5.57 5.57 5.58 5.58 5.59 5.61 5.63 5.64 5.66 5.67 5.67 5.67
5.68 5.68 5.70 5.74 5.85
Mean = Sum of observations / Total no. of observations = 276.33 / 50 = 5.5266
Median = Average of 25th and 26th observation = (5.53 + 5.53) / 2 = 5.53
Range = 5.85 - 5.25 = 0.60
First Quartile = Average of 12th and 13th observation = 5.445
Third Quartile = Average of 37th and 38th observation = 5.585
Inter Quartile Range = Third Quartile - First Quartile = 5.585 - 5.445 = 0.14
Variance = Sum of square of mean deviations / 50 = 0.703722 / 50 = 0.01436167
Standard Deviation = Square root of variance = 0.1186357
Thanks.