Measures of Central Tendency and Dispersion in Frequency Distributions

The frequency distribution below represents the weights in pounds of a sample of packages carried last month by a small airfreight company.

Compute the sample mean
Compute the sample mean using the coding method with 0 assigned to the fourth class
Repeat part (b) with 0 assigned to the sixth class
Explain why your answers in parts (b) and (c) are the same

Davis Furniture Company has a revolving credit agreement with the fast National Bank. The loan showed the following ending monthly balances last year:

The company is eligible for a reduced rate of interest if its average monthly balance is over $65,000. Does it qualify?

Dave’s Giveaway Store advertises, “If our average prices are not equal or lower than everyone else’s, you get free.” One of Dave’s customers came into the store one day and threw counter bills of sale for six items she bought from a competitor for an average prices less than Dave’s.

The items cost

$1.29

$2.97

$3.49

$5.00

$7.50

$10.95

Dave's prices for the same six items are $1.35, $2.89, $3.19, $4.98, $7.59, and $11.50. Dave told the customer, "My ad refers to a weighted average prices of these items. Our average is lower because our sales of these items have been:

Is Dave getting himself into or out of trouble by talking about weighted averages?

Lillian Tyson has been the chairperson of the country library committee for 10 years. She contends that during her tenure She has managed the book-mobile repair budget better than her predecessor did.

M. T. Smith travels the eastern United States as a sales representative for a textbook publisher. She is paid on a commission basis related to volume. Her quarterly earnings over the last 3 years are given below.

	1st Quarter	2nd Quarter	3rd Quarter	4th Quarter
Year 1	$10,000	$ 5,000	$25,000	$15,000
Year 2	20,000	10,000	20,000	10,000
Year 3	30,000	15,000	45,000	50,000

Calculate separately M. T.’s average earnings in each of the four quarters.
Calculate separately M. T.’s average quarterly earnings in each of the 3 years.
Show that the mean of the four numbers you found in part (a) is equal to the mean of the three numbers you found in part (b). Furthermore, show that both these numbers equal the mean of all 12 numbers in the data table. (This is M. T.’s average quarterly income over 3 years.)

National Tire Company holds reserve funds in short-term marketable securities. The ending daily balance of the marketable securities account for 2 weeks is shown below.

The production manager of Hinton Press is determining the average time needed to photograph one printing plate. Using a stopwatch and observing the plate makers, he collects the following times.

An average per-plate time of less than 23.0 seconds indicates satisfactory productivity. Should the production manager be concerned?

A Cosmetics manufacturer recently purchased a machine to fill 3-ounce cologne bottles. To test the accuracy of the machine‘s volume setting, 18 trial bottles were run. The resulting volumes (in ounces) for the trials were as follows:

the company does not normally re-calibrate the filling machine for this cologne if the average volume is within 0.04 of 3.00 ounces. Should it re-calibrate ?

Child-Care Community Nursery can continue to be supported by the county social services office as long as the average annual income of the families whose children attend the nursery is below $12,500. The family incomes of the attending children are

$14,500	$15,600	$12,500	$8,600	$7,800
$6,500	$5,900	$10,200	$8,800	$14,300	$13,900

Does Child-Care qualify now for county support?
If the answer to part (a) is no, by how much must the average family income fall for it to qualify?
s yes, by how much can average family income rise and Child-Care still stay eligible?

The owner of pest R Us in interested in building a new store. The owner will build if the average number of animals sold during the first 6 months of 1995 is at least 300 and the overall monthly average for the year is at least 285.

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