# Question about Measures of Central Tendency and Variation

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 attached table provides the weight in grams of a sample of 50 bags produced in one hour by a single machine.

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?

This question has the following supporting file(s):

• Table.doc
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Solution Summary

This solution is comprised of detailed step-by-step calculations and analysis of the given problems related to Statistics and provides students with a clear perspective of the underlying concepts.

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Anwesha Ghosh, MSc

Rating 4.8/5

Active since 2009

BSc, Banaras Hindu University
MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)

Responses 878

"One more question, if you are familiar with the QM for windows program. Can you tell me how I would input the data into the QM program. There are four choices in the program to choose from when I am in the forecasting module. The choices are Time Series Analysis, Least squares simple and multiple regression, Regression projector, or Error analysis. Please let me know how to input the data if you know how to use this program. Thank you. Sonyia"

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"Thank you!! Responses were timely, and cleared my questions right up. I will be able to use this example for a future problem I am working on as well. Linda"

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"Do you have anything to explain the formulas?"

Extracted Content from Question Files:

• Table.doc

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