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# Levels of Measurement Pratice Questions

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18. Refer to the Wage data, which reports information on annual wages for a sample of 100 workers. Also included are variables relating to industry, years of education, and gender for each worker.
a. Which of the 12 variables are qualitative and which are quantitative?
b. Determine the level of measurement for each variable.

Several years ago, a series of TV advertisements reported that "2 out of 3 dentists surveyed indicated they would recommend Brand X toothpaste to their patients." The implication is that 67 percent of all dentists would recommend the product to their patients. What if they surveyed only three dentists? It would certainly not be a true representation of the real situation. The trick is that the manufacturer of the toothpaste could take many surveys of three dentists and report only the surveys of three dentists in which two dentists indicated they would recommend Brand X. This is concealing the information to mislead the public. Further, a survey of more than three dentists is needed, and it must be unbiased and representative of the population of all dentists.
The term average refers to several different measures of central location that we
discuss in Chapter 3. To most people, an average is found by adding the values involved and dividing by the number of values. So if a real estate developer tells a client
An average may not be representative of all the data.that the average home in a particular subdivision sold for \$150,000, we assume that
\$150,000 is a representative selling price for all the homes. But suppose there are only
five homes in the subdivision and they sold for \$50,000, \$50,000, \$60,000, \$90,000,
and \$500,000. We can correctly claim that the average selling price is \$150,000, but
does \$150,000 really seem like a "typical" selling price? Would you like to also know
that the same number of homes sold for more than \$60,000 as less than \$60,000? Or
that \$50,000 is the selling price that occurred most frequently? So what selling price
really is the most "typical"? This example illustrates that a reported average can be
misleading, because it can be one of several numbers that could be used to represent
the data. There is really no objective set of criteria that states what average should be
reported on each occasion. We want to educate you as a consumer of data about how
a person or group might report one value that favors their position and exclude other
values. We will discuss averages, or measures of central location, in Chapter 3.
Sometimes numbers themselves can be deceptive. The mean price of homes
sold last month in the Tampa, Florida, area was \$134,891.58. This sounds like a very
precise value and may instill a high degree of confidence in its accuracy. To report that the mean selling price was \$135,000 doesn't convey the same precision and accuracy. However, a statistic that is very precise and carries 5 or even 10 decimal places is not necessarily accurate.

3-41 High-Low Method
Manchester Foundry produced 45,000 tons of steel in March at a cost of £1,150,000. In April, the foundry produced 35,000 tons at a cost of £950,000. Using only these two data points, determine the cost function for Manchester

Analysis of liquidity and profitability measures of Gateway, Inc. (Check our website
for future updates.) The following summarized data (amounts in thousands) are
taken from the December 31, 1999, and 1998, comparative financial statements of
Gateway, Inc., a direct marketer and distributor of personal computers (PCs) and PCrelated
products:
(Amounts expressed in thousands) 1999 1998
For the Year Ended December 31:
Net sales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \$8,645,561 \$7,467,925
Cost of goods sold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6,745,744 5,921,651
Operating income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595,670 494,227
Net income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \$ 427,944 \$ 346,399
At December 31:
Assets
Cash and cash equivalents . . . . . . . . . . . . . . . . . . . . . . . . . . . . \$1,127,654 \$1,169,810
Marketable securities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208,717 158,657
Accounts receivable, net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646,339 558,851
Inventory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191,870 167,924
Other current assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522,225 172,944
Property, plant, and equipment, net . . . . . . . . . . . . . . . . . . . . . . 745,660 530,988
Intangibles, net . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52,302 65,944
Other noncurrent assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459,921 65,262
Total assets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . \$3,954,688 \$2,890,380
Liabilities and Owners' Equity
Current maturities of long-term obligations . . . . . . . . . . . . . . . . \$ 5,490 \$ 11,415
Accounts payable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 898,436 718,071
Accrued liabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609,132 415,265
Accrued royalties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153,840 167,873
Other current liabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142,812 117,050
Long-term obligations, net of current maturities . . . . . . . . . . . . . 2,998 3,360
Warranty and other liabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . 124,862 112,971
Common stock and additional paid-in capital . . . . . . . . . . . . . . 660,070 367,552
Retained earnings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1,408,852 980,908
Other stockholders' equity . . . . . . . . . . . . . . . . . . . . . . . . . . . . (51,804) (4,085)
Total liabilities and stockholders' equity . . . . . . . . . . . . . . . . . . . \$3,954,688 \$2,890,380
At December 31, 1997, total assets were \$2,039,271 and total stockholders' equity was
\$930,044.
a. Calculate Gateway, Inc.'s working capital, current ratio, and acid-test ratio at
December 31, 1999, and 1998.
b. Calculate Gateway's ROE for the years ended December 31, 1999, and 1998.
c. Calculate Gateway's ROI, showing margin and turnover, for the years ended
December 31, 1999, and 1998.
d. Evaluate the company's overall liquidity and profitability.
e. Gateway, Inc., did not declare or pay any dividends during fiscal 1999 or
fiscal 1998. What do you suppose is the primary reason for this?
Optional continuation of Case 3.18?trend analysis.
The following historical data were derived from Gateway, Inc.'s consolidated financial
statements. (It should be noted that past data are not necessarily indicative of the results
of future operations.)
1995 1996 1997 1998 1999
Net sales . . . . . . . . . . . . . . \$3,676,328 \$5,035,228 \$6,293,680 \$7,467,925 \$8,645,561
Net income . . . . . . . . . . . . . 172,981 250,679 109,797 346,399 427,944
Total assets . . . . . . . . . . . . . 1,124,011 1,673,411 2,039,271 2,890,380 3,954,688
Long-term obligations,
net of current maturities . . 10,805 7,244 7,240 3,360 2,998
f. Are the trends expressed in the above data generally consistent with each other?
g. In your opinion, which of the above trends would be most meaningful to a
potential investor in common stock of Gateway, Inc.? Which trend would be
least meaningful?
h. What other data (trend or otherwise) would you like to have access to prior
to making an investment in Gateway, Inc.?