Assignment01
1. Caculate the mean, median, and mode for each of the following populations of numbers:
a. 17, 23, 19, 20 ,25, 18, 22, 15, 21, 20
b. 505, 497, 501, 500, 507, 510, 501
Soluton:
a
b
N
10
7
MEAN
20
503
MEDIAN
20
501
MODE
20
501
2. Lauren is a college sophomore majoring in business. This semester Lauren is taking courses in
accounting, economics, management information systems, public speaking, and statistics. The
sizes of these classes are, respectively, 350, 45, 35, 25, and 40. Find the mean and the median
of the class sizes. What is a better measure of Lauren’s “typical class size”- the mean or the
median?
Soluton:
Mean = 99 and the median = 40. Median is better measure of typical because of the high
outlier (350).
3. Table 3.4 gives the percentage of homes sold during the fourth quarter of 2006 that a median
income household could afford to purchase at the prevailing mortgage interest rate for six
Texas metropolitan areas. The data were compiled by the National Association of Home
Builders. Calculate the range, variance, and standard deviation of this population of
affordability percentages.
Table 3.4
Soluton:
x
(x – 54)
(x – 54)**2
57.5
3.5
12.25
61.7
32.5
7.7
–21.5
59.29
462.25
67.4
13.4
179.56
55.7
1.7
2.89
49.2
-4.8
23.04
Range = 67.4 – 32.5 = 34.9
Variance = 123.21
Std Deviation = 11.10
sum(x – 54)**2 PopVariance PopStDev
739.28
123.21
11.10
Mean = 54
4. THE BANK CUSTOMER WAITING TIME CASE
The mean and the standard deviation of the sample of 100 bank customer waiting times are
x =5.46 and s=2.475.
a. What does the histogram in Figure 2.16 say about whether the Empirical Rule should be
used to describe the bank customer waiting times?
b. Use the Empirical Rule to calculate estimates of tolerance intervals containing 68.26
percent, 95.44 percent, and 99.73 percent of all possible bank customer waiting times.
c.
Does the estimate of a tolerance interval containing 68.26 percent of all waiting times
provide evidence that at least two-thirds of all customers will have to wait less than eight
minutes for service? Explain your answer.
d. How do the percentages of the 100 waiting times in Table 1.8 that actually fall into the
intervals[ x  s], [ x  2s], [ x  3s] compare to those given by the Empirical Rule?
Do these comparisons indicate that the statistical inferences you made in parts b and c
are reasonably valid ?
Figure 2.16
Table 1.8 Waiting Times (in Minutes) for the Bank Customer Waiting Time Case
Soluton:
a.It is somewhat reasonable.
b.
[ x  s]  [5.46  2.475]  [2.985,7.935]
[ x  2s]  [5.46  2(2.475)]  [0.51,10.41]
[ x  3s]  [5.46  3(2.475)]  [  1.965,12.885]
c.
Yes, because the upper limit of the 68.26% interval is less than 8 minutes.
d.
66% fall into [ x  s], 97% fall into [ x  2s] , 100% fall into [ x  3s] .
Yes, they are reasonably valid.