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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