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1. Statistical Abstracts (117th edition) reports gasoline excise taxes, in cents per gallon, in the
west (mountain region) as follows:
28
26 9 22 19 18 19 24
Find the mean, the median, and the mode of these taxes.
2. In the process of tuna fishing, porpoises are sometimes accidentally caught and killed. A U.S.
oceanographic institute wants to study the number of porpoises killed in this way. Records from
eight commercial tuna fishing fleets gave the following information about the number of
porpoises killed in a three month period:
2 6 18 9 0 15 3 10
(a) Find the range.
(b) Find the sample mean.
(c) Find the sample standard deviation.
3. City Hospital has a temporary shortage of nurses, so nurses have been working overtime. A
random sample of six nurses reported that the number of overtime hours they worked last week
were:
7 2 4 5 4 3
(a) Compute the mode, the median and the mean for this data set.
(b) Compute the range and standard deviation.
(c) Suppose that a recording error occurred and the data value of 7 was supposed to be a 2.
Replace 7 by 2 in the data. Recalculate the mode, the median and the mean and comment on the
changes produced in the averages by the change in the data.
4. The members of a random sample of 61 Pittsburgh policemen were asked how many years
(rounded to the nearest year) they had served on the city’s police force. The results follow. x
represents the number of years of service and f is the number of policemen.
(a) Estimate the mean number of years of service.
(b) Estimate the standard deviation for the number of years of service.
5. The Statistical Abstract (117th edition) reports the number of hours per year individuals spent
watching television for 1990 through 1995. Information is given for independent TV stations
and for basic cable.
Independent Stations:
340 227 159 162 172 183
Basic Cable:
260 340 359 375 388 468
(a) Compute the median, the population mean and the population standard deviation for
independent stations.
(b) Compute the median, the population mean and the population standard deviation for basic
cable.
(c) Compute the coefficient of variation for both data sets.
(d) What do these numbers tell you about the two distributions?
6. Twenty-four people were asked to rate the flavor of Jane’s Jams ’n’ Jellies brand grape jelly,
on a scale of 1 to 10. The results follow:
8 7 6 9 9 5 3 8
10 9 8 8 6 5 6 7
8 9 1 9 7 8 6 2
(a) Give the five-number summary.
(b) Make a box-and-whisker plot.
7. Complete a 5% trimmed mean for the following set of ages (in years) of giant tortoises:
5 12 16 24 33
7
9 13 42 62 21 41
29 20 36
3 17 81 50 22
8. Home Security Systems is studying the time utilization of its sales force. A random sample of
40 sales calls showed that the representatives spend an average (mean) time of 42 minutes on the
road for each sales call. The standard deviation of the call times is 5 minutes.
(a) Compute the coefficient of variation (CV) for this data.
(b) Use Chebyshev’s Theorem to find the smallest time interval in which we can expect to find
at least 75% of the data.
9. Which data set results in the following box-and-whisker plot?
[A] 5 9 6 6 7 4
[B] 5 9 8 6 7 1
[C] 5 9 8 6 7 4
[D] 4 9 8 6 7 4
[E] 5 7 8 6 7 4
10. McElroy Discount Fashions claims to have a fairly low mark-up percent on the items they
sell. A random sample of 50 items showed the mark-up percent over cost to be (in percents):
15 21 22 25 27 27 27 28 29 31
33 35 36 36 37 37 37 42 42 42
45 46 47 48 49 49 51 51 51 52
53 55 55 58 59 61 65 67 68 71
72 72 72 72 72 75 75 77 78 85
(a) Find the interquartile range.
(b) Give a five-number summary of the data.
(c) Make a box-and-whisker plot for the data.
Reference: [3.1.2]
[1] Mean = 20.6; median = 20.5; mode = 19
Reference: [3.1.8]
[2] Range = 18; x = 7.88; s = 6.36
Reference: [3.1.13]
[3] (a) Mode = 4; median = 4; mean = 4.17
(b) Range = 5; sample standard deviation = 1.72
(c) Mode: none; median = 3.5; mean = 3.33
The mode no longer exists since both 4 and 2 occur the maximum number of times. The mean
changed quite a bit because the largest data value changed.
Reference: [3.1.57]
[4] (a) Mean  10.38 years.
(b) Standard deviation  6.62 years
Reference: [3.1.23]
[5] (a) Median = 177.5;  = 207.2;  = 63.53
(b) Median = 367.0;  = 365.0;  = 61.81
(c) Independent stations: CV = 30.7%; Basic cable: CV = 16.9%
(d) The number of people watching basic cable TV is generally greater than the number
watching independent TV stations and there is less variation in the data for basic cable TV.
Reference: [3.1.65]
[6] (a) Five-number summary = (1, 6, 7.5, 8.5, 10)
(b)
Reference: [3.1.15]
[7] 5% trimmed mean: 25.5 years
Reference: [3.1.72]
[8] (a) CV = 11.9%
(b) Interval from 32 minutes to 52 minutes
Reference: [3.1.74]
[9] [C]
Reference: [3.1.67]
[10] (a) IQR = 31
(b) Five-number summary: (15, 36, 49, 67, 85)
(c)