# 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.

1. Compute the sample mean
2. Compute the sample mean using the coding method with 0 assigned to the fourth class
3. Repeat part (b) with 0 assigned to the sixth class
4. 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?

Child-Care Community Nursery is eligible for a county social services grant as long as the average age of its children stays below 9. If these data represent the ages of all the children currently attending Child-Care, do they qualify for the grant?

 8 5 9 10 9 12 7 12 13 7 8

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

These data represent the ages patients admitted to a small hospital on February 28, 1996.
1. Construct a frequency distribution with classes 40-49, 50-59, etc.
2. Compute the sample mean from the frequency distribution.
3. Compute the sample mean from the raw data.
4. Compare parts (b) and (c) and comment on your anser

The Frequency distributions below represents the time in seconds needed to serve a sample of customers by cashiers at Bulls Eye Discount Store in December 1996.

 Time (in seconds) Frequency 20–29 6 30–39 16 40–49 21 50–59 29 60–69 25 70–79 22 80–89 11 90–99 7 100–109 4 110–119 0 120–129 2
1. Compute the sample mean
2. Compute the sample mean using the coding method with 0 assigned to the 70–79 class.

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.

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 ?

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?

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.