Descriptive Statistics
156 Chapter 3 Descriptive Statistics: Numerical Measures

penalty to the owner (The Wall Street Journal, January 30, 2006). The tax penalty for a

sample of 20 small business owners follows:

WEB file 820 270 450 1010 890 700 1350 350 300 1200
390 730 2040 230 640 350 420 270 370 620
Penalty

a. What is the mean tax penalty for improperly filed employment tax returns‘?

b. What is the standard deviation‘?

o. Is the highest penalty, $2040, an outlier?

d. What are some of the advantages of a small business owner hiring a payroll service
company to handle employee payroll services, including the employment tax returns?

65. Morningstar tracks the performance of a large number of companies and publishes an eval-
uation of each. Along with a variety of financial data, Morningstar includes a Fair Value
estimate for the price that should be paid for a share of the company’s common stock. Data

WEB e for 30 companies are available in the file named FairValue. The data include the Fair Value
estimate per share of common stock, the most recent price per share, and the earning per
Fawalue share for the company (Morningsrar Stocks 500, 2008).

a. Develop a scatter diagram for the Fair Value and Share Price data with Share Price on
the horizontal axis. What is the sample correlation coefficient, and what can you say
about the relationship between the variables‘?

b. Develop a scatter diagram for the Fair Value and Earnings per Share data with Earn-
ings per Share on the horizontal axis. What is the sample correlation coefficient, and
what can you say about the relationship between the variables?

66. According to an annual consumer spending survey, the average monthly Bank of America

Visa credit card charge was $1838 (U.S. Air-ways Arrache’ Magazine, December 2003). A

sample of monthly credit card charges provides the following data.

236 1710 1351 825 “£450
file 316 4135 1333 1584 387
was 991 3396 170 1428 1688

a. Compute the mean and median.

b. Compute the first and third quartiles.

c. Compute the range and interquartile range.

d. Compute the variance and standard deviation.

e. The skewness measure for these data is 2.12. Comment on the shape of this distribu-
tion. Is it the shape you would expect‘? Why or why not‘?

f. Do the data contain outliers?

67. The U.S. Census Bureau provides statistics on family life in the United States, including
the age at the time of first man-iage, current marital status, and size of household

(U.S. Census Bureau website, March 20, 2006). The following data show the age at the

time of first marriage for a sample of men and a sample of women.

Men 26 23 28 25 2?.-’ 30 26 35 28
WEB fii€ 21 24 27 29 3o 27 32 27 25
Ages Women 20 28 23 30 24 29 26 25
22 22 25 23 27 26 19

a. Determine the median age at the time of first marriage for men and women.

b. Compute the first and third quartiles for both men and women.

c. Twenty-five years ago the median age at the time of first marriage was 25 for men and
22 for women. What insight does information provide about the decision of when
to marry among young people today‘?