Deck 5: Displaying and Describing Quantitative Data

Question 1

Below is the five number summary of the hourly wages ($) for sales managers.
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

Answer 1

a. Decrease
b. Stay the same
c. Increase
d. Stay the same
e. Increase

Question 2

Consider the following to answer the question(s) below:
Below is a histogram and the five number salary for salaries (in $) for a sample of marketing managers.
Do the data contain any outliers as determined by a boxplot?

A) only at the upper end
B) only at the lower end
C) at the upper and the lower ends
D) There are no outliers.
E) It cannot be determined.

Answer 2

A

Question 3

Consider the following to answer the question(s) below:
Below is a histogram and the five number salary for salaries (in $) for a sample of marketing managers.
Suppose the marketing manager who was earning $129,420 got a raise and is now earning $140,000. Which one of the following statements is true?

A) The mean would increase.
B) The median would increase.
C) The range would stay the same.
D) The IQR would increase.
E) The IQR would decrease.

Answer 3

A

Question 4

Consider the following to answer the question(s) below:
The table below shows closing share prices for a small sample of companies.

The standard deviation in closing share prices is

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

Question 5

Consider the following to answer the question(s) below:
Below is a histogram and the five number salary for salaries (in $) for a sample of marketing managers.
The upper and lower "fences" for a boxplot of these data are

A) $47,636 and $113,807
B) $43,934.5 and $110,105.5
C) $54,963 and $99,077
D) $36,607.5 and $124,835.5
E) $58,664.5 and $102,778.5

Question 6

The boxplots show monthly sales revenue figures ($ thousands) for a discount office supply company with locations in three different regions in Canada. (Atlantic, Central 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 7

Below is a histogram of salaries (in $) for a sample of marketing managers. Comment on the shape of the distribution.

Question 8

The table below shows data on total assets ($ million) for a sample of a bank's branches.
For the data on total assets ($ million) for the sample provided:
a. Calculate the mean.
b. Calculate the standard deviation.
c. Standardize the asset value of the third branch (find the z score). Interpret its meaning.

Question 9

The table below 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 10

Below is the five-number summary of salaries (in $) for a sample of marketing managers.
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 11

Below 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 12

Consider the following to answer the question(s) below:
Below is a histogram and the five number salary for salaries (in $) for a sample of 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 13

Consider the following to answer the question(s) below:
Below is a histogram and the five number salary for salaries (in $) for a sample of marketing managers.
The shape of this distribution is

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

Question 14

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 histograms below. 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 15

Consider the following to answer the question(s) below:
Below is a histogram and the five number salary for salaries (in $) for a sample of marketing managers.
The IQR for these data is

A) $83,060
B) $22,057
C) $69,693
D) $77,020
E) $14,566

Question 16

The boxplots below show the closing share prices for a sample of companies on the first trading days in August 2007 and in August 2002. a. For which day was the median closing share price higher?
b. For which day were the closing share prices more variable? Explain.
c. Which distribution is more symmetric? Explain.

Question 17

Below is the five number summary of the hourly wages ($) for advertising / promotion managers.
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 18

The table below shows data on total assets ($ million) for a sample of a bank's branches. Prepare a stem and leaf display. Comment on the shape of the distribution.

Question 19

Consider the following to answer the question(s) below:
The table below shows closing share prices for a small sample of companies.

The mean closing share price is

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

Question 20

Below is the five-number summary of salaries (in $) for a sample of marketing managers.
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 21

If a distribution for a quantitative variable is thought to be nearly symmetric with very little variation, and a boxplot is created for this distribution, which of the following is true?

A) The box will be quite wide but the whiskers will be very short.
B) The whiskers will be about half as long as the box is wide.
C) There will be no whiskers.
D) The lower whisker will be the same length as the upper whisker.
E) The left and right-hand edges of the box will be approximately equal distance from the median.

Question 22

The asking price for homes on the real estate market in Winnipeg has a mean value of $286,455 and a standard deviation of $11,200. The mean and standard deviation in asking price for homes in Moncton are $188,468 and $8,230, respectively. Recently, one home sold in each city where the asking price for each home was $225,000. Based on these data, what conclusions can be drawn?

A) The two homes have the same z-score.
B) The distribution of the asking prices is symmetric in both cities.
C) The home sold in Winnipeg is relatively further from its mean than the home sold in Moncton.
D) The asking price of homes in Moncton is less variable than those in Winnipeg.
E) The z-score for Winnipeg is higher than that of Moncton.

Question 23

The advantage of using the interquartile range versus the range as a measure of variation is

A) It is easier to compute.
B) It uses all the data when computed.
C) It always gives a closer measure of the true variation.
D) It is the more powerful measure of spread.
E) It is less affected by unusual or extreme observations in the data.

Question 24

The asking price for homes in the Winnipeg real estate market has a mean value of $286,455 and a standard deviation of $11,200. The mean and standard deviation in asking price for homes in Moncton are $188,468 and $8,230, respectively. Recently, one home sold in each city where the asking price for each home was $225,000. Based on these data, which of the following statements is true?

A) The coefficient of variation for Winnipeg is more than that for Moncton.
B) The Moncton home has a standardized value that is relatively closer to zero.
C) The coefficient of variation is the same for both cities.
D) The Winnipeg home has a standardized value that is relatively closer to zero.
E) Both homes have the same z-score.

Question 25

Which of the following best describes the difference between stem-and-leaf diagrams and histograms?

A) There is no difference.
B) The histogram shows the shape and spread but not the centre.
C) The histogram shows the shape, centre, and spread of the distribution while the stem-and-leaf does not.
D) The stem-and-leaf diagram shows less information than a histogram.
E) The stem-and-leaf diagram shows more information by showing the individual values.

Question 26

Consider the following to answer the question(s) below:
The boxplots below show monthly sales revenue figures ($ thousands) for a discount office supply company with locations in three different regions of Canada. (Atlantic, Central and West).
Which of the following statements is true?

A) The Central region has the lowest sales revenues.
B) The Central region 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) The Atlantic region has the lowest mean sales.

Question 27

Consider the following to answer the question(s) below:
The boxplots below show monthly sales revenue figures ($ thousands) for a discount office supply company with locations in three different regions of Canada. (Atlantic, Central 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 Central region has the smallest IQR.
D) The Atlantic region has the most variable sales revenues.
E) The Central region has the least variable sales revenues.

Question 28

A sample of families with children at a local school is found to have a mean of 3.2 members per family. The mode number of family members is 2 and the median number is 2.0. Based on this information, which statement is true?

A) The population mean is greater than 3.2.
B) The distribution is symmetric.
C) The distribution is right-skewed.
D) The distribution is left-skewed.
E) The distribution is bell-shaped.

Question 29

Sample data were collected on the number of hours per day students spent at the computer. Which one of the following statements is true?

A) Females have the larger mean.
B) Males have the larger range.
C) The coefficient of variation is larger for males.
D) The coefficient of variation is larger for females.
E) The variation of males is larger.

Question 30

Consider the following to answer the question(s) below:
The table below shows closing share prices for a small sample of companies.

The z score for the share price for Matsushita Electronic Components is

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

Question 31

Below is a time series graph for monthly closing stock prices of 3M Dental Products. Which of the following statements is true?

A) The data are stationary.
B) The data show an upward trend.
C) A histogram would provide a good representation of these data.
D) The data show a downward trend.
E) A boxplot would provide a good representation of this data.

Question 32

A student recently wrote an entrance exam and was informed that his score placed him at the 80th percentile. This indicates that

A) 80 students who also took the exam scored below him.
B) he scored as high or higher than 80 percent of all those who wrote the exam.
C) he was in the bottom 20 percent of those who wrote the exam.
D) his z score was 80.
E) his exam mark was 80 out of 100.