Chapter Problems
Problem 1
Supermarket / Price X1 / $1.31
2 / 1.35
3 / 1.26
4 / 1.42
5 / 1.31
6 / 1.33
Total / $7.98
A comparison shopper employed by a large grocery chain recorded these prices for a 340-gram jar of Kraft blackberry preserves at a sample of six supermarkets selected at random.
a.Compute the arithmetic mean.
b.Compute the median.
c.Compute the mode.
Exercise 3.1Check your answers against those in the ANSWER section.
The number of semester credit hours for seven part-time college students is: 8, 5, 4, 10, 8, 3, and 4.
Compute the:
a.meanb.medianc.mode
Problem 2
From 1988 to 2002 the number of hospital beds sold by Wagoner Enterprises increased from 5 to 300. Compute the mean annual percent increase in the number of hospital beds sold.
Exercise 3.2Check your answers against those in the ANSWER section.
In 1987, thirty hectares of forest was valued at $475 per hectare. In 2002 the forest was valued at $1850 per hectare.
What is the geometric mean annual percent increase in value?
Problem 3
A sample of the amounts spent in November for propane gas to heat homes of similar sizes in Duluth revealed these amounts (to the nearest dollar):
$191$212$176$129$106$92$108$109$103$121$175$194
What is the range? Interpret your results.
Problem 4
Using the heating cost data in Problem 3, compute the mean deviation.
Problem 5
HourlyWages / Number
f
$8up to$10 / 3
$10 up to$12 / 6
$12 up to$14 / 12
$14 up to$16 / 10
$16 up to$18 / 7
$18 up to$20 / 2
40
The hourly wages for a sample of plumbers were grouped into the following frequency distribution. Since the wages have been grouped into classes, we refer to the following distribution as being grouped data.
a.Compute the arithmetic mean.
b.Compute the mode.
Exercise 3.3Check your answers against those in the Answer section. / Exports / Frequency
The annual exports of 50 medium-sized manufacturers were organized into a frequency distribution. (Exports are in $ millions).
Compute the:
a.meanb.mode / $6 up to $9 / 2
9 up to 12 / 8
12 up to 15 / 20
15 up to 18 / 14
18 up to 21 / 6
Problem 6
At Sarasota College there are 10 instructors, 12 assistant professors, 20 associate professors, and 5 professors. Their average annual salaries are $34,000, $45,000, $58,000, and $68,000, respectively. What is the weighted mean salary?
Exercise 3.4Check your answers against those in the ANSWER section.
During the past month an electronics store sold 31 model EL733 calculators for $30 each, 42 model EL480 calculators for $10 each, 47 model FX115 calculators for $20 each, and 63 model BA35 calculators for $24 each.
What is the weighted mean price of the calculators?
Problem 7
Using the same heating cost data in Problem 3, compute the variance and the standard deviation.
Exercise 3.5Check your answers against those in the ANSWER section.
The manager of a fast-food restaurant selected several cash register receipts at random. The amounts spent by customers were $12, $15, $16, $10, and $27. Compute the:
a.range
b.the mean deviation
c.the sample variance
d.the sample standard deviation
Problem 8
Age to theNearest Month / Number of
Personal Computers
20 up to 25 / 3
25 up to 30 / 5
30 up to 35 / 10
35 up to 40 / 7
40 up to 45 / 4
45 up to 50 / 1
The office manager of the Mallard Glass Company is investigating the ages in months of the company’s personal computers currently in use. The ages of 30 units selected at random were organized into a frequency distribution. Compute the range.
Problem 9
Using the ages of the personal computer equipment in Problem 8, compute the variance and the standard deviation.
Problem 10
A sample of the business faculty at state supported institutions in Ohio revealed the mean income to be $52,000 for 9 months with a standard deviation of $3,000. Use Chebyshev's Theorem and the Empirical Rule to estimate the proportion of faculty who earn more than $46,000 but less than $58,000.
Problem 11
Recall from Problem 10, a study of business faculty at provinicially supported institutions in Ontario revealed that the arithmetic mean salary for nine months is $52,000 and the standard deviation of the sample is $3,000. The study also showed that the faculty had been employed a mean of 15 years with a standard deviation of 4 years. How does the relative dispersion in the distribution of salaries compare with that of the lengths of service?
Exercise 3.7Check your answers against those in the ANSWER section.
An automobile dealership pays its salespeople a salary plus a commission on sales. The mean biweekly commission is $990, the median $950, and the standard deviation $70.
a.Estimate the percent of salespeople that earn more than $885, but less than $1095.
b.Is the distribution of commissions positively skewed, negatively skewed, or symmetrical?
Problem 12
Listed below are the selling prices (in thousands of dollars) of a sample of 15 homes sold by agents working in Churchill, Manitoba.
$20$56$65$17$26$90$13$27
$16$68$86$80$50$25$92
Determine the first and third quartiles and the median for the data.
Problem 13
Use the selling price of homes data from Problem 12 to develop a box plot.
Exercise 3.8Check your answers against those in the ANSWER section.
Listed below are the selling prices (in thousands of dollars) of a sample of 19 homes sold by agents working in Timmins, Ontario.
$86$61$148$81$39$142$140$65$28$85
$90$92$25$50$85$85$82$120$137
Determine the following:
a.the first quartileb.the third quartilec.the mediand.Draw a box plot for the data.