A quality characteristic of interest for a tea-bag-filling process is the weight
ID: 3252594 • Letter: A
Question
A quality characteristic of interest for a tea-bag-filling process is the weight of the tea in the individual bag. In this example, the label on the package indicates that, on average, there are 5.5 grams of tea in a bag. 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 170bags a minute). If the bags are under filled: - Customers may not be able to brew the tea as strong as they wish. - The company may be in violation of the truth-in labeling laws. If the bags are over filled: - The company is giving away product. The data below provide the weight in grams of a sample 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?
PLEASE INCLUDE THE FORMULAS So I can do it in excell OR a picture of the work done in EXCEL so I can do it. Thank u
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)
Mean = AVERAGE() = 5.525
Median = MEDIAN() = 5.53
b)
For quartile command use = QUARTILE.EXC(Select data set, )
1 for first quartile , 2 for second quartile, 3 for third quartile
First quartile = QUARTILE.EXC(,1) = 5.4475
Second quartile = QUARTILE.EXC(,2) = 5.53
Third quartile = QUARTILE.EXC(,3) = 5.595
c)
Now to find range = maximum observation - minimum observation = 5.85 - 5.25 = 0.6
Interquartile range = Third quartile - first quartile = 5.595 - 5.4475 = 0.1475
Variance = VAR.S() = 0.012695
Standard deviation = STDEV.S() = 0.11267
Coefficient variation = (Standard deviation / mean ) *100 = 2.039306
Extra tea = population mean - sample mean = 5.52 - 5.5 = 0.25
Here the 0.25 kg more tea is given per bag.
e)Comany should care about variation because as variation minimum it is better to company.
so company should care about variation.
d)Related Questions
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