Descriptive Statistics of a Survey

[1] The computer giant IBM has 329,373 employees and 637,133 stockholders. A vice president plans to conduct a survey to study the number of shares held by individual stockholders.

Are the numbers of shares held by stockholders discrete or continuous?

Identify the level of measurement (nominal, ordinal, interval, ratio) for the numbers of shares held by stockholders.

If the survey is conducted by telephoning 20 randomly selected stockholders in each of the 50 United States, what type of sampling (random, systematic, convenience, stratified, cluster) is being used?

What is wrong with gauging stockholder views about employee benefits by mailing a questionnaire that IBM stockholders could complete and mail back?

[2] A bank branch located in a commercial district of a city has developed an improved process for serving customers during the noon-to-1:00 p.m. peak period. The waiting time in minutes (defined as the time customer enters the line to the time he/she is served) of all customers during this hour is recorded over a period of one week. A random number sample of 15 customers is selected, and the results are as follows:
4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20
4.50 6.10 0.38 5.12 6.46 6.19 3.79

Compute the following statistics. You may attach an Excel output instead of manual calculations.
Quantity Measurement
Mean
Median
Mode
Variance
Sample standard deviation
Sample variance
Range
Coefficient of Variation (CV)

Compute the following statistics. You may attach an Excel output instead of manual calculations.
Minimum Q1 Median Q3 Maximum

Construct the box-and-whisker diagram for the data. You may attach an Excel output instead of manual drawing.

Describe the shape of the distribution of the bank branch located in a commercial district of a city using the box plot. Explain why you would think that the shape you describe happens with this type of data.

Is there any data point that should be considered as an outlier for this data set? Explain why.

As a customer walks into the branch office during the lunch hour, she asks the branch manager how long she can expect to wait. The branch manager replies, “Almost certainly less than five minutes.” On the basis of the results of (a) through (e), evaluate the accuracy of this statement.

[3] In an article in the November 1993 issue of Quality Progress, Barbara A. Cleary reports on improvements made in a software supplier’s responses to customer calls. In this article, the author states:
In an effort to improve its response time for these important customer-support-calls, an inbound telephone inquiry team was formed at PQ Systems, Inc., a software and training organization in Dayton, Ohio. The team found that 88 percent of the customers’ calls were already being answered immediate by the technical support group, but those who had to be called back had to wait an average of 56.6 minutes. No customer complaints had been registered, but the team believed that this response rate could be improved.
As part of its improvement process, the company studied the disposition of complete and incomplete calls to its technical support analysis. A call is considered complete if the customer’s problem has been resolved; otherwise the call is incomplete. Below is the summary table for the
incomplete customer calls.

Action by Technical Support Analysts Percentage
Required customer to get more data 29.17
Required more investigation by us 28.12
Callbacks 21.87
Required development assistance 12.50
Required administrative help 4.17
Determined as actually a new problem 4.17

Construct a Pareto chart
What percentage of incomplete calls required “more investigation” by the analyst or “administrative help?”
Can you make a suggestion to improve responses?

[4] The Corner Convenience Store kept track of the number of paying customers it had during the noon hour each day for the last 150 days. The following are the resulting statistics rounded to the nearest integer:
X ̅ (sample mean) = 95 s (sample standard deviation) = 12
X ̃ (median) = 97 Q1 (third quartile) = 85
m (mode) = 99 Q3 (third quartile) = 107
R (range) = 56

What number of paying customers did the Corner Convenience Store serve during the noon hours more often than any other number? Explain how you determined your answer.

On how many days was there between 85 and 107 paying customers during the noon hour? Explain how you determined your answer.

For how many of the 150 days was the number of paying customers within three standard deviations from the mean? Explain how you determined your answer.