Question

A quality characteristic of interest for a flour-bag-filling process is the weight of the flour in the individual bags. If the bags are under filled, 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 10 pounds of flour in a bag. If the average amount of flour in a bag exceeds the label weight, the company is giving away product. Getting an exact amount of flour in a bag is problematic because of variation in the temperature and humidity inside the factory, and the extremely fast filling operation of the machine (approximately 150 bags a minute). The following table provides the weight in pounds of a sample of 70 bags produced in one hour by a single machine:
10.31	9.74	10.01	10.04	10.10	10.45	10.37	10.19	10.10	9.74
10.37	9.85	10.38	10.11	10.11	9.92	9.72	9.78	9.97	10.50
9.84	10.22	9.70	9.75	10.02	10.19	10.07	10.36	10.39	9.83
10.14	10.42	10.11	9.73	10.31	10.40	9.86	10.45	10.45	10.25
10.28	9.82	9.74	10.23	10.41	10.20	9.81	10.06	10.32	10.43
10.24	9.73	10.06	10.31	10.10	10.34	9.78	9.88	10.05	9.96
9.85	10.27	10.32	10.35	10.06	10.07	9.86	10.37	10.47	10.37
a) Compute the mean by using the function, =AVERAGE()
Compute the median using =MEDIAN()
	Median
b) Compute the first and third quartiles, by using either =QUARTILE.INC() or =QUARTILE.EXC() for both the First and Third Quartiles
	First Quartile
	Third Quartile
c) Compute the range, interquartile range, variance, standard deviation, and coefficient of variation.
	Range				Use the functions, =MAX()-MIN()
	Interquartile range
	Variance				Use the function =VAR.S()
	Standard deviation				Use the function =STDEV.S()
	Coefficient of variation. Coefficient of variation is the standard deviation divided by the mean. Note that coefficient of variation should be expressed in percentage

Answer 1

The question is solved using Excel as per the requirement. The excel sheet is attached as well.

a) Mean = 10.11

Median = 10.11

b) First Quartile = 9.86

Third Quartile = 10.34

c) Range = 0.80

Interquartile Range = 0.48

Variance = 0.06

Standard Deviation = 0.24

Coefficient of Variance = 2.40%