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Chapter 2:
Describing
Data: Numerical
2.1
Cruise
agency – number of weekly specials to the Caribbean : 20, 73, 75, 80, 82
a. Compute the mean, median and mode
median = middlemost observation = 75
mode
= no unique mode exists
b.
The median best describes the
data due to the presence of the outlier of 20.
This skews the distribution to the left.
The agency should first check to see if the value ‘20’ is correct.
2.2
Number of
complaints: 8, 8, 13, 15, 16
a.
Compute the mean number of
weekly complaints:
b.
Calculate the median =
middlemost observation = 13
c.
Find the mode = most frequently
occurring value = 8
2.3
CPI
percentage growth forecasts: 3.0, 3.1,
3.4, 3.4, 3.5, 3.6, 3.7, 3.7, 3.7, 3.9
a.
Compute the sample mean: 
b.
Compute the sample median =
middlemost observation: 
c.
Mode = most frequently
occurring observation = 3.7
2.4
Department
store % increase in dollar sales: 2.9, 3.1, 3.7, 4.3, 5.9, 6.8, 7.0, 7.3, 8.2,
10.2
a.
Calculate the mean number of
weekly complaints: 
b.
Calculate the median =
middlemost observation: 
2.5 Percentage of total
compensation derived from bonus payments: 10.2, 13.1, 15, 15.8, 16.9, 17.3,
18.2, 24.7, 25.3, 28.4, 29.3, 34.7
a. Median % of total
compensation from bonus payments = 
b. Mean %
2.6
Daily sales
(in hundreds of dollars): 6, 7, 8, 9, 10, 11, 11, 12, 13, 14
a.
Find the mean, median, and mode
for this store
Mean = 
Median =
middlemost observation = 
Mode = most
frequently occurring observation = 11
b.
Find the five-number summary
Q1 = the value
located in the 0.25(n + 1)th ordered position
= the value located in the 2.75th
ordered position
= 7
+ 0.25(8 –7) = 7.25
Q3 = the value
located in the 0.75(n + 1)th ordered position
= the value located in the 8.25th
ordered position
= 12 + 0.75(13 –12) = 12.75
Minimum = 6
Maximum = 14
Five - number summary:
minimum < Q1
< median < Q3 < maximum
6 < 7.25 < 10.5 < 12.75
< 14
2.7
Find the measures of central tendency for the
number of imperfections in a sample of 50 bolts
Mean number
of imperfections = 
= 0.44 imperfections
per bolt
= 0.44 imperfections
per bolt
Median = 0
(middlemost observation in the ordered array)
Mode = 0
(most frequently occurring observation)
2.8
Ages of 12
students: 18, 19, 21, 22, 22, 22, 23, 27, 28, 33, 36, 36
a.
b.
Median = 22.50
c.
Mode = 22
2.9
a.
First quartile, Q1 = the value
located in the 0.25(n + 1)th ordered position
= the value located in the 39.25th ordered position
= 2.98 + 0.25(2.98 –2.99) = 2.9825
Third quartile, Q3 = the value located in the
0.75(n + 1)th ordered position
= the value located in the 117.75th
ordered position
= 3.37 + 0.75(3.37 –3.37) = 3.37
b.
30th percentile =
the value located in the 0.30(n + 1)th ordered position
= the value located in the 47.1th
ordered position
=
3.10 + 0.1(3.10 –3.10) = 3.10
80th percentile = the value located in the 0.80(n + 1)th
ordered position
= the value located in the 125.6th
ordered position
=
3.39 + 0.6(3.39 –3.39) = 3.39
2.10
a. 
b. Median = 9.0
c. The distribution is slightly skewed to the
left since the mean is less than the median.
d. The five-number summary
Q1 = the value located in the 0.25(n + 1)th
ordered position
= the value located in the 8.5th
ordered position
= 6
+ 0.5(6 – 6) = 6
Q3 = the value
located in the 0.75(n + 1)th ordered position
= the value located in the 25.5th
ordered position
= 10 + 0.5(11 –10) = 10.5
Minimum = 2
Maximum = 21
Five - number summary:
minimum < Q1 < median < Q3 <
maximum
2 <
6 < 9 < 10.5 < 21
2.11
a. 
. The mean volume of
the random sample of 100 bottles (237 mL) of a new suntan lotion was 236.99 mL.
. The mean volume of
the random sample of 100 bottles (237 mL) of a new suntan lotion was 236.99 mL.
b. Median = 237.00
c. The distribution is symmetric. The mean and median are nearly the same.
d. The five-number summary
Q1 = the value located in the 0.25(n + 1)th
ordered position
=
the value located in the 25.25th ordered position
= 233 + 0.25(234 – 233) = 233.25
Q3 = the value
located in the 0.75(n + 1)th ordered position
= the value located in the 75.75th
ordered position
= 241 + 0.75(241 –241) = 241
Minimum = 224
Maximum = 249
Five - number summary:
minimum < Q1 < median < Q3 <
maximum
224 < 233.25 < 237 <
241 < 249
2.12
The
variance and standard deviation are
|
xi
|
DEVIATION ABOUT THE MEAN,
 |
SQUARED DEVIATION ABOUT THE MEAN,
 |
|
6
|
–1
|
1
|
|
8
|
1
|
1
|
|
7
|
0
|
0
|
|
10
|
3
|
9
|
|
3
|
–4
|
16
|
|
5
|
–2
|
4
|
|
9
|
2
|
4
|
|
8
|
1
|
1
|
 |
 |
 |
Statistics
for Business and Economics, 8e (Newbold)
Chapter 2 Describing Data: Numerical
1) If you are interested in comparing
variation in sales for small and large stores selling similar goods, which of
the following is the most appropriate measure of dispersion?
A) the range
B) the interquartile range
C) the standard deviation
D) the coefficient of variation
Answer:
D
Difficulty: Easy
Topic:
Measures of Variability
AACSB:
Reflective Thinking Skills
Course LO:
Compare and contrast methods of summarizing and describing data
2) Suppose you are told that the mean of a
sample is below the median. What does this information suggest about the
distribution?
A) The distribution is symmetric.
B) The distribution is skewed to the right
or positively skewed.
C) The distribution is skewed to the left
or negatively skewed.
D) There is insufficient information to
determine the shape of the distribution.
Answer:
C
Difficulty: Easy
Topic:
Measures of Central Tendency and Location
AACSB:
Reflective Thinking Skills
Course LO:
Compare and contrast methods of summarizing and describing data
3) For the following scatter plot, what
would be your best estimate of the correlation coefficient?
A) -0.8
B) -1.0
C) 0.0
D) -0.3
Answer:
A
Difficulty: Moderate
Topic:
Measures of Relationships Between Variables
AACSB:
Analytic Skills
Course
LO: Compare and contrast methods of
summarizing and describing data
4) Given a set of 25 observations, for
what value of the correlation coefficient would we be able to say that there is
evidence that a relationship exists between the two variables?
A) 
≥ 0.40
≥ 0.40
B) ≥ 0.35
≥ 0.35
C) ≥ 0.30
≥ 0.30
D) ≥ 0.25
≥ 0.25
Answer:
A
Difficulty: Moderate
Topic:
Measures of Relationships Between Variables
AACSB:
Analytic Skills
Course LO:
Identify and apply formulas for calculating descriptive statistics
5) Which of the following statements is
true about the correlation coefficient and covariance?
A) The covariance is the preferred measure
of the relationship between two variables since it is generally larger than the
correlation coefficient.
B) The correlation coefficient is a
preferred measure of the relationship between two variables since its
calculation is easier than the covariance.
C) The covariance is a standardized
measure of the linear relationship between two variables.
D) The covariance and corresponding
correlation coefficient are represented by different signs, one is negative
while the other is positive and vice versa.
Answer:
C
Difficulty: Moderate
Topic:
Measures of Relationships Between Variables
AACSB:
Reflective Thinking Skills
Course LO:
Compare and contrast methods of summarizing and describing data
6) For the following scatter plot, what
would be your best estimate of the correlation coefficient?
A) 1.0
B) 0.7
C) 0.3
D) 0.1
Answer:
B
Difficulty: Moderate
Topic:
Measures of Relationships Between Variables
AACSB:
Analytic Skills
Course
LO: Compare and contrast methods of
summarizing and describing data
7) Which of the following descriptive
statistics is least affected by outliers?
A) mean
B) median
C) range
D) standard deviation
Answer:
B
Difficulty: Easy
Topic:
Measures of Central Tendency and Location
AACSB:
Reflective Thinking Skills
Course LO:
Compare and contrast methods of summarizing and describing data
8) Which of the following statements is
true?
A) The correlation coefficient is always
greater than the covariance.
B) The covariance is always greater than
the correlation coefficient.
C) The covariance may be equal to the
correlation coefficient.
D) Neither the covariance nor the
correlation coefficient can be equal to zero.
Answer:
C
Difficulty: Moderate
Topic:
Measures of Relationships Between Variables
AACSB:
Reflective Thinking Skills
Course LO:
Compare and contrast methods of summarizing and describing data
9) Which measures of central location are
not affected by extremely small or extremely large data values?
A) arithmetic mean and median
B) median and mode
C) mode and arithmetic mean
D) geometric mean and arithmetic mean
Answer:
B
Difficulty: Moderate
Topic:
Measures of Central Tendency and Location
AACSB:
Reflective Thinking Skills
Course LO:
Compare and contrast methods of summarizing and describing data
10) Suppose you are told that sales this
year are 30% higher than they were six years ago. What has been the average
annual increase in sales over the past six years?
A) 5.0%
B) 4.5%
C) 4%
D) 3.5%
Answer:
B
Difficulty: Moderate
Topic:
Measures of Central Tendency and Location
AACSB:
Analytic Skills
Course
LO: Identify and apply formulas for calculating
descriptive statistics
11) Suppose you are told that sales this
year are 20% higher than they were five years ago. What has been the annual
average increase in sales over the past five years?
A) 5.2%
B) 4.7%
C) 4.2%
D) 3.7%
Answer:
D
Difficulty: Moderate
Topic:
Measures of Central Tendency and Location
AACSB:
Analytic Skills
Course LO:
Identify and apply formulas for calculating descriptive statistics
12) Suppose you are told that over the
past four years, sales have increased at rates of 10%, 8%, 6%, and 4%. What has
been the average annual increase in sales over the past four years?
A) 7.0%
B) 6.7%
C) 6.4%
D) 6.5%
Answer:
A
Difficulty: Moderate
Topic:
Measures of Central Tendency and Location
AACSB:
Analytic Skills
Course LO:
Identify and apply formulas for calculating descriptive statistics
13) Suppose you are told that the average
return on investment for a particular class of investments was 7.8% with a
standard deviation of 2.3. Furthermore, the histogram of the distribution of returns
is approximately bell-shaped. We would expect that 95 percent of all of these
investments had a return between what two values?
A) 5.5% and 10.1%
B) 0% and 15%
C) 3.2% and 12.4%
D) 0.9% and 14.7%
Answer:
C
Difficulty: Moderate
Topic:
Measures of Central Tendency and Location
AACSB:
Analytic Skills
Course LO:
Identify and apply formulas for calculating descriptive statistics
14) What is the relationship among the
mean, median, and mode in a positively skewed distribution?
A) They are all equal.
B) The mean is always the smallest value.
C) The mean is always the largest value.
D) The mode is the largest value.
Answer:
B
Difficulty: Moderate
Topic:
Measures of Central Tendency and Location
AACSB:
Reflective Thinking Skills
Course
LO: Compare and contrast methods of
summarizing and describing data
15) The manager of a local RV sales lot
has collected data on the number of RVs sold per month for the last five years.
That data is summarized below:
|
# of Sales
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
|
# of Months
|
2
|
6
|
9
|
13
|
21
|
7
|
2
|
What is the weighted mean number of sales
per month?
A) 3.31
B) 3.23
C) 3.54
D) 3.62
Answer:
B
Difficulty: Moderate
Topic:
Weighted Mean and Measures of Grouped Data
AACSB:
Analytic Skills
Course LO:
Identify and apply formulas for calculating descriptive statistics
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