Problem no. 4 In order to better understand the interactions that take place between salespeople and customers. Ronald P. Willett and Allan L. Pennington (1966) monitored the interactions of appliance salespeople and customers on the floor of a large department store. Part of their research involved observing the length of time customers and salespeople interacted prior to the close of the sale or the departure of the customer. The data below, adapted from the article, are the lengths of time (in minutes) from the first customer-salespeople contact to the close of the sale or the customer's departure for 132 customers who completed their appliance purchase either at the time they were observed or within the following 2 weeks. Instances where a purchase was made by the customer at the time he or she was observed are denoted with an asterisk.

1.0* 33.3 40.1 6.0* 1.7 4.5* 3.0 5.1* 7.4* 37.0

0.7 15.0* 27.2* 10.9 18.7* 13.3* 30.0* 41.3* 44.4* 9.7

15.0 12.3 16.2 7.4* 17.6* 14.9 15.1* 32.2 1.9* 7.0*

5.4* 8.4 15.5 14.0* 40.0 6.1 28.7 38.1 30.5 8.1*

7.6 7.9 25.4* 12.2* 22.3 7.8* 29.2 30.5 34.6* 4.1*

7.0* 10.3 21.9 0.4* 25.6* 3.3 26.4* 39.2* 42.3 10.0*

1.1 10.1* 17.4* 14.9 20.1* 9.0* 27.7 42.1 48.6 41.6

11.1 31.8 25.1* 12.0* 16.9* 26.0 27.7 47.6* 35.1 11.0*

15.0* 35.4 30.0* 14.2 19.2* 39.9 23.0 43.1 38.2 49.1*

12.8* 10.9* 20.6* 7.7 50.1 8.0* 24.8 35.0* 8.1* 13.0

118.4 8.9* 60.2* 105.2* 11.0 15.9 20.1* 3.2 8.8 77.1

18.0* 0.8 12.5 69.1 11.1 30.0 12.4 1.5 14.2* 7.9*

17.7* 0.9 8.4 81.0 10.5 26.2 18.4 6.0 15.9 13.5

66.1* 98.2

Required

1. Construct a relative frequency histogram for each of the following data sets:

a. The complete set of 132 times.

b. The set of times associated with customers who made appliance

purchases at the time they were being observed.

c. The set of times associated with customers who made the appliance purchases at a later date.

2. Describe any differences you detect between the histograms of parts 1(b) and 1(c).

3. Suggest possible explanations for the differences you noted in part 2.

4. Develop a stem-and-leaf display for the complete set of data using the hundreds for the stem and the one-tenths for the leaf. Compare this to the frequency histogram.

5. Illustrate the complete set of data as a greater than and a less than ogive using both absolute and relative frequency values.

6. Using the complete raw data determine the maximum value, minimum value, range, mean, median, standard deviation assuming the data was a sample and standard deviation taking the data correctly as a population. Determine also the

modal value and indicate the order of modality (single, bi, tri, etc.)

7. Determine the quartile values for the complete data and use these to develop a box and whisker plot. Are there any outliers? If so, what are those? What can you say about the distribution of this data?

8. Determine the percentile values for the complete data and plot these on a histogram.

9. Calculate for the mean, median, mode, standard deviation, variance, range, coefficient of variation and skewness coefficient of the complete grouped data set of 132 times. Compare these values for those obtained from Question no. 6.