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Chapter 2: Q37E (page 94)
Explain how the relationship between the mean and median provides information about the symmetry or skewness of the data’s distribution.
If the mean is to the right, the distribution is skewed to the right.
If the mean is to the left, the distribution is skewed to the left.
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The amount spent on textbooks for the fall term was recorded for a sample of five university students. The following data were observed: \(400, \)350, \(600, \)525, and $450. Calculate each of the following values for this data:
a.The sample mean
b.The sample median
c.The sample range
d.The standard deviation
In terms of percentiles, define QL, QM and QU
A sample data set has a mean of 57 and a standard deviation of 11. Determine whether each of the following sample measurements are outliers.
a.65
b.21
c.72
d.98
Microsoft program security issues. To help its users combat malicious attacks (e.g., worms, viruses) on its computer software, Microsoft periodically issues a security bulletin that reports the software affected by the vulnerability. In Computers & Security (July 2013), researchers focused on reported security issues with three Microsoft products: Office, Windows, and Explorer
a. In a sample of 50 security bulletins issued in a recent year, 32 reported a security issue with Windows, 6 with Explorer, and 12 with Office. Construct a pie chart to describe the Microsoft products with security issues. Which product had the lowest proportion of security issues?
b. The researchers also categorized the security bulletins according to the expected repercussion of the vulnerability. Categories were Denial of service, Information disclosure, Remote code execution, Spoofing, and Privilege elevation. Suppose that of the 50 bulletins sampled, the following numbers of bulletins were classified into each respective category: 6, 8, 22, 3, 11. Construct a Pareto diagram to describe the expected repercussions from security issues. Based on the graph, what repercussion would you advise Microsoft to focus on?
Consider the horizontal box plot shown below.
a.What is the median of the data set (approximately)?
b.What are the upper and lower quartiles of the data set (approximately)?
c.What is the interquartile range of the data set (approximately)?
d.Is the data set skewed to the left, skewed to the right, or symmetric?
e.What percentage of the measurements in the data set lie to the right of the median? To the left of the upper quartile?
f.Identify any outliers in the data.
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