Lesson 5.1.1
5-7. The Hookenslise Corporation is in the midst of union negotiations. Labor claims that the company’s
average salary is $28,000 while management claims it is $32,000. If they are using the same set of data,
how can their averages be different? How could such a large difference have occurred?
[ Labor is using the median and management is using the mean. A few large
“outliers,” such as executives with high salaries. ]
5-8. The following are test scores from a difficult chemistry test. Calculate the mean and median from
each set of data:
a. 62, 68, 75, 60, 72, 62, 67
[ mean = 66.5 points , median = 67 points ]
b. 60, 62, 96, 68, 72, 62, 67
[ mean = 69.5, median = 67 ]
c. The highest score in the second set is 96. What effect does this score have on the mean and
median for the set?
[ The median is not influenced by the high score, but the mean is. ]
5-9. Create a set of data in which:
a. The median is much higher than the mean.
[ Sample answer: 1, 80, 80 ]
b. The mean is much higher than the median.
[ Sample answer: 1, 1, 27 ]
5-10. Consider the data set: 24, 5, 1, 27, 41, 3, 40, 6, 43, 10
a. Add a value to the data set that will keep the mean the same.
[ 20 ]
b. Add a value to the data set that will keep the median the same.
[ 17 ]
c. Add a value to the data set that will increase the mean.
[ Any number > 20 ]
d. Add a value to the data set that will decrease the median.
[ Any number < 17 ]
Lesson 5.1.2
For each problem below, determine whether a histogram or dot plot would best display
the data and then display the data using that representation. Next, describe the center,
shape, and spread of the data distribution. [ See answers following the problems. ]
5-20. The electrical current in milli-amperes flowing through a sample of microcircuits.
132, 130, 133, 137, 134, 137, 137, 133, 130, 133, 132, 135, 135, 135
5-21. The GPAs of a sample of 30 community college applicants were selected and
listed
below.
2.78, 2.83, 2.69, 3.46, 2.63, 2.73, 3.54, 2.50, 1.87, 2.72, 1.58, 3.49, 2.81, 3.75,
2.46,4.29, 2.34, 2.46, 3.30, 3.67, 2.44, 3.10, 3.80, 3.42, 2.99, 3.16, 2.32, 1.87,
3.89, 3.19
5-22. A sample of 22 newborn boys at St. Rudolf’s Hospital had the following lengths in
centimeters.
50.6, 51.1, 51.4, 50.4, 50.1, 53.8, 48.8, 49.0, 52.4, 47.1, 53.2, 46.9, 51.8, 50.0,
49.3, 52.0, 54.4, 47.7, 48.5, 50.6, 46.4, 51.8
5-23. The speeds (in miles per hour) of motorists ticketed during one day on a five-mile
stretch of highway.
83, 75, 85, 77, 80, 79, 84, 82, 82, 83,78, 78, 80, 80, 81, 85, 80, 83, 85, 74, 78,
85, 83, 84, 82
Lesson 5.1.3
5-36. Group X: 49, 54, 52, 58, 61, 72, 73, 78, 73, 82, 83, 73, 61, 67, and 68 years
Group Y: 65, 35, 48, 29, 57, 87, 94, 68, 86, 73, 58, 74, 85, 91, 88, and 97 years.
Create a parallel box plot for the ages of these two groups of people. For each
group, answer the following questions:
a. What is the five-number summary for each group?
[ Group X: 49, 58, 68, 73, 83; Group Y: 29, 57.5, 73.5, 87.5, 97 ]
b. Does the mean accurately represent the middle of the data? Why or why not?
[ Group X: mean = 66.93 Yes, because there are no outliers.; Group Y: mean =
70.94 Yes, because there are no outliers. ]
c. Describe the center, shape, spread, and outliers.
[ Group X: center = mean = 66.93 years, shape = uniform, spread = IQR = 15 years,
no outliers; Group Y: center = mean = 70.94, shape = relatively uniform with a bit of
a left skew, spread = IQR = 30, technically no outliers, but 29 looks like it could
possibly be an outlier ]
5-37. Given a set of data: 265, 263, 269, 259, 267, 264, 253, 275, 264, 260, 273, 257, and 291 rpm
a. Find the five-number summary.
[ 253, 259.5, 264, 271, 291 ]
b. Find the interquartile range (IQR).
[ 11.5 ]
c. Make a box plot of the data.
[ See plot at right. ]
d. Describe the center, shape, spread, and outliers.
[median = 264, shape = right (positively) skewed, spread = IQR = 11.5, outlier = 291]
5-38. Compare the two data sets in the parallel box plot at right. Compare the center, shape, and spread
of the data sets. Write a possible scenario for the data.
[ Both data sets have a similar median (in Set B it is a bit greater). Set B has a
larger range/spread in the data. Set A has much less spread and is fairly
symmetric. Possible Scenario: Test scores where Class A had a large portion of
the class scoring C’s. Class B had many high C’s, but some very low scores as
well. ]
5-39. The manager of Widgets R Us has two teams of employees and wants to know which team is
working the “best.” The assistant manager gathered data for the average number of widgets made per
team member per shift and presented it to the manager in the form of a parallel box plot, shown at right.
The manager is confused. Help them decide which team is working the “best.”
[ Answers vary: Their “average” may be a bit lower, but Team 1 has less spread
and is therefore more consistent. ]