Question

Define each question as being or not being a statistical question and explain why. (75–150 words or 1–2 paragraphs)

Joan Horton is a building contractor whose company builds many homes every year. In planning for each job, Joan needs some idea about the direct labor hours per square foot required to build a home. She has collected sample information on the labor hours for 10 jobs during the past year. (300 words or 4 paragraphs)

Job	1	2	3	4	5	6	7	8	9	10
Hours	245	291	353	118	152	402	351	242	595	173

• Calculate the mean for this sample. How can Joan use this information?
• Calculate the median from this sample. If Joan had to select the mean or the median as the estimate of direct labor hours, what factors about each statistic should she consider before making the decision?
• Calculate the sample variance and standard deviation. How can Joan use these values in planning future jobs?
• One of Joan’s competitors, J.M. Sawyer, has numbers claiming that his crews average 350 hours per square foot, with a standard deviation of 50. Sawyer further claims that his company is more consistent in direct labor hours applied to houses than Horton’s company. Who is right, and why?

The weekly total of hours for the servers and the cooks for a small restaurant are listed below. Find the range, variance, and standard deviation for each set. Which set of data is more variable? (75–150 words or 1–2 paragraphs)

Week	1	2	3	4	5	6	7	8	9	10
Servers	823	837	858	791	812	814	832	862	833	826
Cooks	752	764	754	774	771	745	736	816	792	793

Answer 1

Job	Hours
1	245
2	291
3	353
4	118
5	152
6	402
7	351
8	242
9	595
10	173
mean	292.2
median	268
variance	19984.18
standard deviation	141.3654

Formulas in Excel

Job	Hours
1	245
2	291
3	353
4	118
5	152
6	402
7	351
8	242
9	595
10	173
mean	=AVERAGE(B1:B11)
median	=MEDIAN(B1:B11)
variance	=VAR(B1:B11)
standard deviation	=STDEV(B1:B11)

Calculate the mean for this sample. How can Joan use this information?

= 292.2

Calculate the median from this sample. If Joan had to select the mean or the median as the estimate of direct labor hours, what factors about each statistic should she consider before making the decision?

median = 268

Calculate the sample variance and standard deviation. How can Joan use these values in planning future jobs?

sample variance = 19984.18

sample standard deviation = 141.3654

One of Joan’s competitors, J.M. Sawyer, has numbers claiming that his crews average 350 hours per square foot, with a standard deviation of 50. Sawyer further claims that his company is more consistent in direct labor hours applied to houses than Horton’s company. Who is right, and why?

There is sufficient evidence that Sawyer's company is more consistent in direct labor hours applied to houses than Horton’s company.