Deck 5: Displaying and Describing Quantitative Data

Question 1

Analyze data of quantitative variables.

-The following table shows total assets ($ billion) for a small sample of U.S. banks.
The standard deviation for these data is $$\begin{array} { | l | l | } \hline { \text { BANK } } & \text { ASSETS (\$ billion) } \\\hline \text { Bank of New York } & 88 \\\hline \text { Regions Financial } & 80 \\\hline \text { Fifth Third Bank } & 58 \\\hline \text { State Street Bank and Trust } & 92 \\\hline \text { Branch Banking and Trust Company } & 81 \\\hline \text { Chase Bank } & 70 \\\hline \text { Key Bank } & 89 \\\hline \text { PNC Bank } & 84 \\\hline\end{array}$$

A) $12.78 billion.
B) $ 11.27 billion.
C) $ 127.01 billion.
D) $ 21.67 billion.
E) $ 34 billion.

Answer 1

$ 11.27 billion.

Question 2

Analyze scatterplots and correlation coefficients.
For the data on total assets ($ billion) for a small sample of U.S. banks provided in the
previous question:
a. Calculate the mean.
b. Calculate the standard deviation.
c. Standardize the asset value of Fifth Third Bank (find the z score). Interpret its
meaning.

Answer 2

97 (this value is approximately 2 standard deviations below the mean).

Question 3

Analyze data of quantitative variables.

-The following table shows total assets ($ billion) for a small sample of U.S. banks.
The mean for these data is $$\begin{array} { | l | l | } \hline { \text { BANK } } & \text { ASSETS (\$ billion) } \\\hline \text { Bank of New York } & 88 \\\hline \text { Regions Financial } & 80 \\\hline \text { Fifth Third Bank } & 58 \\\hline \text { State Street Bank and Trust } & 92 \\\hline \text { Branch Banking and Trust Company } & 81 \\\hline \text { Chase Bank } & 70 \\\hline \text { Key Bank } & 89 \\\hline \text { PNC Bank } & 84 \\\hline\end{array}$$

A) $ 80.25 billion.
B) $ 100.35 billion.
C) $ 75.68 billion.
D) $ 84 billion.
E) $ 89 billion.

Answer 3

$ 80.25 billion.

Question 4

Following is a time series graph for monthly closing price of 3M Dental Products
stock (beginning June 2005).
a. Are the closing prices for shares of 3M Dental Products from June 2005 through
August 2007 stationary? Explain.
b. Would a histogram provide a good summary of these stock prices? Explain.

Question 5

Following is the five number summary of the hourly wages ($) for advertising /
promotion managers displayed in question 1.
a. Would you expect the mean salary for this sample of marketing managers to be higher
or lower than the median? Explain.
b. Which would be a more appropriate measure of central tendency for these data, the
mean or median? Explain.
c. Calculate the range.
d. Calculate the IQR.

Question 6

Interpret displays of distributions.
The following boxplots show monthly sales revenue figures ($ thousands) for a
Discount office supply company with locations in three different regions of the U.S.
(Northeast, Southeast, and West). Which of the following statements is true?

A) The northeast has the lowest mean sales revenue.
B) The southeast has the lowest median sales revenue.
C) The west has the lowest mean sales revenue.
D) The west has the lowest median sales revenue.
E) None of the above.

Question 7

Following is the five number summary of the hourly wages ($) for sales managers
displayed in question 1.
Suppose there had been an error and that the lowest hourly wage for sales managers was
$18.50 instead of $20.94. Indicate how this change would affect the following summary
statistics (increase, decrease, or stay about the same):
a. Mean
b. Median
c. Range
d. IQR
e. Standard deviation

Question 8

Compare results using standardization.

-The following table shows total assets ($ billion) for a small sample of U.S. banks.
The z- score for the total assets of Fifth Third Bank is $$\begin{array} { | l | l | } \hline { \text { BANK } } & \text { ASSETS (\$ billion) } \\\hline \text { Bank of New York } & 88 \\\hline \text { Regions Financial } & 80 \\\hline \text { Fifth Third Bank } & 58 \\\hline \text { State Street Bank and Trust } & 92 \\\hline \text { Branch Banking and Trust Company } & 81 \\\hline \text { Chase Bank } & 70 \\\hline \text { Key Bank } & 89 \\\hline \text { PNC Bank } & 84 \\\hline\end{array}$$

A) 1.25.
B) -1.25.
C) -2.5.
D) 1.97.
E) -1.97.

Question 9

The following boxplots show monthly sales revenue figures ($ thousands) for a
discount office supply company with locations in three different regions of the U.S.
(Northeast, Southeast, and West).

a. Which region has the highest median sales revenue?
b. Which region has the lowest median sales revenue?
c. Which region has the most variable sales revenue values? Explain.

Question 10

Analyze data of quantitative variables.

-The following table shows closing share prices for a small sample of companies. The
Mean closing share price is $$\begin{array} { | l | c | } \hline \text { COMPANY } & \text { CLOSING SHARE PRICE - 08/07 } \\\hline \text { 3M Dental Products } & 86.95 \\\hline \text { Tyco Electronics Power Systems } & 47.45 \\\hline \text { Kyocera America Inc. } & 94.10 \\\hline \text { Pfizer Inc. } & 22.39 \\\hline \text { Xerox Company } & 17.56 \\\hline \text { Northrop Grumman Corporation } & 75.81 \\\hline \text { Lockheed Martin Maritime Systems } & 100.17 \\\hline \text { Sony DADC } & 51.91 \\\hline \text { Matsushita Electronic Components } & 17.91 \\\hline \text { Foster Wheeler Environmental Corp. } & 55.67 \\\hline\end{array}$$

A) $31.23.
B) $44.65.
C) $56.99.
D) $62.19.
E) $75.77.

Question 11

Interpret summary statistics.

-Based on the five number summary (shown below) for salaries of U.S. marketing
Managers, the IQR is $$\begin{array} { | c | c | c | c | c | } \hline \text { Min } & \text { Q1 } & \text { Median } & \text { Q3 } & \text { Max } \\\hline 46360 & 69693 & 77020 & 91750 & 129420 \\\hline\end{array}$$

A) $83,060.
B) $22.057.
C) $69,693.
D) $77.020.
E) $14,566.

Question 12

Analyze data of quantitative variables.

-The following table shows closing share prices for a small sample of companies. The
Standard deviation in closing share prices is $$\begin{array} { | l | c | } \hline \text { COMPANY } & \text { CLOSING SHARE PRICE - 08/07 } \\\hline \text { 3M Dental Products } & 86.95 \\\hline \text { Tyco Electronics Power Systems } & 47.45 \\\hline \text { Kyocera America Inc. } & 94.10 \\\hline \text { Pfizer Inc. } & 22.39 \\\hline \text { Xerox Company } & 17.56 \\\hline \text { Northrop Grumman Corporation } & 75.81 \\\hline \text { Lockheed Martin Maritime Systems } & 100.17 \\\hline \text { Sony DADC } & 51.91 \\\hline \text { Matsushita Electronic Components } & 17.91 \\\hline \text { Foster Wheeler Environmental Corp. } & 55.67 \\\hline\end{array}$$

A) $31.43.
B) $44.65.
C) $56.99.
D) $62.19.
E) $75.77.

Question 13

Analyze scatterplots and correlation coefficients.
Suppose the marketing manager who was earning $129,420 got a raise and is now
earning $140,000. Indicate how this change would affect the following summary
statistics (increase, decrease, or stay about the same):
a. Mean
b. Median
c. Range
d. IQR
e. Standard deviation

Question 14

Compare results using standardization.

-The following table shows closing share prices for a small sample of companies. The
Z score for the share price for Matsushita Electronic Components is $$\begin{array} { | l | c | } \hline \text { COMPANY } & \text { CLOSING SHARE PRICE - 08/07 } \\\hline \text { 3M Dental Products } & 86.95 \\\hline \text { Tyco Electronics Power Systems } & 47.45 \\\hline \text { Kyocera America Inc. } & 94.10 \\\hline \text { Pfizer Inc. } & 22.39 \\\hline \text { Xerox Company } & 17.56 \\\hline \text { Northrop Grumman Corporation } & 75.81 \\\hline \text { Lockheed Martin Maritime Systems } & 100.17 \\\hline \text { Sony DADC } & 51.91 \\\hline \text { Matsushita Electronic Components } & 17.91 \\\hline \text { Foster Wheeler Environmental Corp. } & 55.67 \\\hline\end{array}$$

A) 1.24.
B) 2.34.
C) -2.34.
D) -3.00.
E) -1.24.

Question 15

Describe displays of distributions.
Below is a histogram of salaries (in $) for a sample of U.S. marketing managers. The
Most appropriate measure of central tendency for these data is the

A) median.
B) mean.
C) mode.
D) range.
E) standard deviation.

Question 16

Interpret displays of distributions.
The following boxplots show monthly sales revenue figures ($ thousands) for a
Discount office supply company with locations in three different regions of the U.S.
(Northeast, Southeast, and West). Which of the following statements is false?

A) The west has the most variable sales revenues.
B) The west has the largest IQR.
C) The southeast has the smallest IQR.
D) The northeast has the most variable sales revenues.
E) The southeast has the least variable sales revenues.

Question 17

The following table shows closing share prices (on the first trading day of August,
2007) for a small sample of companies.
a. Calculate the mean.
b. Calculate the standard deviation
c. Standardize the share price for Matsushita Electronic Components (find the z score).
Interpret its meaning.

Question 18

Data were collected on the hourly wage ($) for two types of marketing managers: (1)
advertising / promotion managers and (2) sales managers. The results were used to create
the following histograms.
a. Describe the hourly wage distribution for advertising / promotion managers.
b. Describe the hourly wage distribution for sales managers.
c. Compare the hourly wages for the two types of marketing managers based on the
histograms.

Question 19

Describe displays of distributions.
Below is a histogram of salaries (in $) for a sample of U.S. marketing managers. The
Shape of this distribution is

A) symmetric.
B) bimodal.
C) right skewed.
D) left skewed.
E) normal.

Question 20

Compare results using standardization.
The ASQ (American Society for Quality) regularly conducts a salary survey of its
Membership, primarily quality management professionals. Based on the most recently
Published mean and standard deviation, a quality control specialist calculated the z-score
Associated with his own salary and found it was -2.50. This tells him that his salary is

A) 2 and a half times more than the average salary.
B) 2 and a half times less than the average salary.
C) is 2.5 standard deviations above the average salary.
D) is 2.5 standard deviations below the average salary.
E) much higher than the average salary.

Question 21

Interpret summary statistics.

-Consider the five number summary of hourly wages ($) for a sample of advertising /
Promotion managers. Suppose there had been an error and that the lowest hourly wage
Was $15.50 instead of $19.64. This would result in $$\begin{array} { | c | c | c | c | c | } \hline \text { Min } & \text { Q1 } & \text { Median } & \text { Q3 } & \text { Max } \\\hline 19.64 & 29.36 & 34.18 & 40.86 & 57.26 \\\hline\end{array}$$

A) an increase in the median.
B) an increase in the standard deviation.
C) a decrease in the range.
D) a decrease in the IQR.
E) an increase in the mean.

Question 22

Interpret summary statistics.

-Consider the five number summary of hourly wages ($) for a sample of sales
Managers. The range for these data is $$\begin{array} { | c | c | c | c | c | } \hline \text { Min } & \text { Q1 } & \text { Median } & \text { Q3 } & \text { Max } \\\hline 20.94 & 37.64 & 44.77 & 49.34 & 67.11 \\\hline\end{array}$$

A) $11.70
B) $46.17
C) $67.11
D) $20.94
E) $44.77

Question 23

Interpret summary statistics.

-Consider the five number summary of hourly wages ($) for a sample of sales
Managers. Suppose the mean hourly wage is $38.50. What can we say about the shape
Of the distribution? $$\begin{array} { | c | c | c | c | c | } \hline \text { Min } & \text { Q1 } & \text { Median } & \text { Q3 } & \text { Max } \\\hline 20.94 & 37.64 & 44.77 & 49.34 & 67.11 \\\hline\end{array}$$

A) The distribution of hourly wages for sales managers is symmetric.
B) The distribution of hourly wages for sales managers is skewed right.
C) The distribution of hourly wages for sales managers is skewed left.
D) The distribution of hourly wages for sales managers is bimodal.
E) None of the above.

Question 24

Interpret summary statistics.

-Consider the five number summary of hourly wages ($) for a sample of sales
Managers. The IQR for these data is $$\begin{array} { | c | c | c | c | c | } \hline \text { Min } & \text { Q1 } & \text { Median } & \text { Q3 } & \text { Max } \\\hline 20.94 & 37.64 & 44.77 & 49.34 & 67.11 \\\hline\end{array}$$

A) $11.70
B) $46.17
C) $67.11
D) $20.94
E) $44.77