BA 240 Winter 2006
W. Li
01/19/2006
Practice Exam 1 Solution
Problem 1:
Consider following sample of 16 quantitative measurements:
88, 53, 64, 59, 72, 91, 59, 68, 76, 55, 62, 65, 84, 62, 59, 77
Ordered Data: 53, 55, 59, 59, 59, 62, 62, 64, 65, 68, 72, 76, 77, 84, 88, 91
a)
Calculate the three Measures of Central Tendency.
Mean:
375
.
68
16
91
88
...
59
55
53
n
x
x
i
Median:
5
.
64
2
65
54
M
Mode:
59
b)
Describe the shape (skew) using part a). Justify your answer.
Skew to RIGHT since Mean > Median
c)
Calculate the Fivenumber Summary.
Min
Q1
Median
Q3
Maximum
53
59 (4
th
#)
64.5
77 (13
th
#)
91
d)
Calculate the standard deviation.
76931
.
11
15
75
.
2077
1
2
n
x
x
s
i
(11.77)
e)
Find the
zscore
for the Minimum and the Maximum.
306
.
1
769
.
11
375
.
68
53
s
x
x
z
922
.
1
769
.
11
375
.
68
91
s
x
x
z
f)
Assume data is normal. Construct an interval that will include about 68% of the data set above.
Consider using Empirical Rule: 68% means within the range of
s
x
:
144
.
80
,
606
.
56
)
769
.
11
(
375
.
68
s
x
g)
Count how many data actually fall into the interval in part f), and what is the percentage
of the data?
11 data fall into (56.606, 80.144). Thus, 11/16 = 68.75% of data fall into the range.
Problem 2
:
Fred keeps track of his commute times. He has found that they have a normal
shaped distribution with a mean of 46.2 minutes and a standard deviation of 11
minutes.
a)
What percentage of his commute times is between 13.2 minutes and 79.2 minutes?
11
,
2
.
46
s
x
s
x
3
)
11
(
3
2
.
46
2
.
13
s
x
3
)
11
(
3
2
.
46
2
.
79
From Empirical Rule, 99.7% (100%) of time is between 13.2 minutes and 79.2
minutes (within the range
s
x
3
).
Practice Exam 1 Solution
1
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BA 240 Winter 2006
W. Li
01/19/2006
b)
What percentage of time does it take him at most 68.2 minutes to get to work?
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