Question

Job	1	2	3	4	5	6	7	8	9	10
Hours	245	291	353	118	152	402	351	242	595	173
Average	Median	Standard Deviation	Variance
292.2	268	141.37	19984.18

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?

Answer 1

1) Joans direct labor hours applied to houses have mean = 292.2 & std deviation 141.37

2) J.M. Sawyer direct labor hours applied to houses have 350 hours per square foot, with a standard deviation of 50.

To compare we will use The coefficient of variation (CV)

The coefficient of variation (CV) is a statistical measure of the dispersion of data points in a data series around the mean. The coefficient of variation represents the ratio of the standard deviation to the mean, and it is a useful statistic for comparing the degree of variation from one data series to another, even if the means are drastically different from one another.

CV = Standard deviation / mean

1) CV for Joans

CV1 =  141.37 / 292.2 = 0.4838 = 48.38 %

2) For J.M. Sawyer's direct labor hours applied to houses have 350 hours per square foot, with a standard deviation of 50.

CV2 = 50/350 = 0.1429 = 14.29%

Here CV for J.M. Sawyer is lower than CV for joan's company.

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