FRST 231 Introduction to Biometrics
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Introduction to Biometrics (FRST 231)
Department of Forest Resources Management
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Lab 1 |
1) A lumber sawmill in British Columbia had a very prosperous year. The following observa- tions represent the number of hours of employee overtime required to meet consumer de- mand for each of the last 50 weeks (the data has been sorted from low to high).
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21.0 |
34.5 |
41.0 |
46.2 |
51.0 |
54.5 |
60.0 |
63.4 |
70.0 |
75.5 |
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21.0 |
35.5 |
41.3 |
49.9 |
51.4 |
55.0 |
60.3 |
65.4 |
70.0 |
80.0 |
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29.9 |
36.2 |
41.3 |
50.0 |
51.4 |
58.0 |
60.8 |
67.3 |
70.9 |
80.5 |
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31.2 |
37.0 |
44.6 |
50.2 |
53.0 |
59.9 |
60.8 |
67.7 |
71.6 |
88.4 |
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31.8 |
39.7 |
45.0 |
50.7 |
53.2 |
60.0 |
61.5 |
69.9 |
75.0 |
89.9 |
a) [Canvas entry] Based on the numbers above, calculate:
• Range (R) (1 decimal):
• Number of classes (c) according to Sturge’s rule (no decimals):
• Class width (CW) (no decimals):
b) [PDF upload] Complete the frequency distribution table below based on the observations above. Start by drawing horizontal lines to accommodate the number of classes (c) you
calculated. Use the lowest value from the data above to establish your starting point (SP).
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Class limits |
Class boundaries |
Midpoint |
Frequency |
Relative frequency |
Cumulative frequency |
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c) [PDF submission] Draw a histogram that illustrates the frequency distribution above. Don’t forget to include axis labels and units.
d) [PDF upload] Draw a single graph that illustrates both afrequency polygon and a relative frequency polygon for these data (use two axes).
e) [PDF upload] Draw a cummulativefrequency polygon and a relative cumulativefrequen- cy polygon in the same graph.
f) [Canvas entry] Use the best graph from the ones above to estimate how often, in theory, would 50 hours of overtime occur in a 50 week period:
g) [Canvas entry] Use the best graph produced in the previous questions to estimate how often, in theory, would 50 hours or less of overtime occur in a 50 week period.
h) [Canvas entry] Calculate the arithmetic mean from the raw data (2 decimals):
i) [Canvas entry] Identify the modes from the raw data (1 decimal):
j) [Canvas entry] Calculate the median from the raw data (2 decimals):
k) [Canvas entry] Calculate the midrange from the raw data (2 decimal):
l) [Canvas entry] Does the mode from raw data mean much in a dataset like this? Why or why not?
m) [Canvas entry] If you think of the frequency distribution-based concept of the mode, how do you describe this distribution?
n) [Canvas entry] Based on the analysis of this data and assuming that demand remains constant in the upcoming years, what would you do as a manager of the mill?
2023-02-13