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Lab 2 Statistical Analysis of UNR Quad Measurements January 24, 2014 Lab Group 0 Miles Greiner Lab Instructors: Joshua McGuire, Şevki Çeşmeci and Roberto V Bejarano Abstract • Student stride length was measured for two purposes: – To correlate it with student height – To estimate the cost to seed the UNR Quad • 79 Students determined their stride length by counting the number of steps required to traverse a known distance. For the class, student stride length did not appear to be highly correlated with height. This suggests the stride length may not have been accurately determined. • Students determined the long and short dimensions of the Quad by counting the number of steps to traverse those distances and using the measured stride length. The sample average and standard deviation of the cost estimate were $1050 and $220. • For this measurement process, I got a cost estimate of $983. If I want to be 90% sure to have enough money to seed the Quad, I need to budget 1.292 standard deviations above this value, or $1334. • A better technique for estimating the actual stride length will reduce the standard deviation and the cost estimate. Figure 1 Stride Length versus Height • The stride length does not appear to be highly correlated with height. • This suggests the stride length may not have been measured accurately or it may depend on uncontrolled factors Fig. 2 Cost Estimate Histogram • Non of the cost estimates appear to be far out of place. • The cost estimates from the 79 students who measured the quad varied from $370 to $1480 Table 1 Measurement and Cost Means and Standard Deviations Units Average Short Dimension, S Long Dimension, L Area, A Cost, C Standard Devation ft 131 15 ft 452 51 ft2 $ 60,000 1050 12,000 220 • The sample mean and standard deviation of the cost estimates are $1050 and $220, respectively Fig. 3 Long Edge Length versus Short Edge Length • These measurements appear to be highly correlated (students who got large L measurements systematically got large S measurements) • Data on the right of the graph are from students whose stride length during the calibration process was longer than that during the Quad measurement • If the stride lengths during the calibration and measurement were the same, we would not expect this data to show a significant slope Budget to seed Quad • My best cost estimate was $983. • To be 90%-certain that I have enough money to seed the quad, the cost estimate must be 1.282 standard deviations above my best estimate. • For this measurement process the cost estimate standard deviation is $220, so I should budget $1265 to be 90% sure I have enough. • A better calibration technique will reduce the standard deviation of the process and the cost estimate. End of Sample Report Table 1 Measurement and Cost Means and Standard Deviations (2011, 2013) Average Standard Deviation Short Dimension, S [ft] 130 17 Long Dimension, L [ft] 460 60 Area, A [ft2] 62,000 14000 Cost, C [$] 1082 236 Average Short Dimension [ft] S Long Dimension [ft] L A Area [ft2] Cost [$] C 133 462 23000 1100 Standard Deviation 22 64 19000 300 • The sample mean and standard deviation of the cost estimate from earlier years are roughly the same as for the current year