Module 4 Written Assignment Math 80+80S
Module 4 Written Assignment
Numerical Methods for Describing Data
Name: _____________________________________
Please show all work for this assignment, because you will be graded on the clarity of your explanation as well as the correctness of your work. An answer with no work will receive no credit.
Roman Mint Gold Content
(% by weight)
0.15
0.28
0.17
0.32
0.17
0.36
0.18
0.38
0.20
0.38
0.21
0.42
0.22
0.43
0.23
0.47
0.24
0.50
0.24
1) The measurements in the table at the right are from coins minted in Rome during the first three centuries AD. Historians believe that different mints reveal themselves in different trace element profiles in the coins. Atomic Absorption Spectrometry was used to estimate the % by weight of various elements in these coins, and the % by weight of gold is presented here.
(a) Calculate these numerical summaries.
Mean_________________________
Median_________________________
Standard Deviation_________________________
Interquartile Range_________________________
(b) Construct a skeletal box plot for the data from the previous page.
(c) Using only the data and your responses in parts (a) and (b), would you say this distribution is skewed or approximately symmetric? Justify your response using appropriate statistical terminology.
2) In 1997, a woman sued a computer keyboard manufacturer, charging that her repetitive stress injuries were caused by the keyboard (Genessey v. Digital Equipment Corporation). The jury awarded about $3.5 million for pain and suffering, but the court then set aside that award as being unreasonable compensation. In making this determination, the court identified a “normative” group of 27 similar cases and specified a reasonable award as one within 2 standard deviations of the mean of the awards in the 27 cases. The 27 award amounts were the following, in thousands of dollars. What is the maximum possible amount that could be awarded under the “2-standard deviations rule?”
37
60
75
115
135
140
149
150
238
290
340
410
600
750
750
750
1050
1100
1139
1150
1200
1200
1250
1576
1700
1825
2000
3) To investigate the effects of the insecticide lead arsenate on table wines, 35 bottles of white wine from different wineries in a certain region where the insecticide was used were sample, and the amount of lead (mg/l) was determined by carbon rod atomic absorption spectrophotometry. The findings were as follows.
0.30
0.35
0.37
0.41
0.43
0.45
0.47
0.31
0.36
0.39
0.41
0.43
0.45
0.47
0.34
0.36
0.39
0.41
0.44
0.45
0.47
0.34
0.37
0.39
0.42
0.44
0.45
0.47
0.34
0.37
0.40
0.43
0.44
0.46
0.50
(a) Compute the mean and standard deviation of the amount of lead.
(b) Find the percentages of the observations falling in the intervals and . Are these percentages close to those given by the Empirical Rule? Why or why not?
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