Question

Problems with a telephone line that prevent a customer from receiving or making calls are disconcerting to both the customer and the telephone company. These problems can be of two types: those that are located inside a central office and those located on lines between the central office and the customer's equipment. The following data represent samples of 20 problems reported to two different offices of a telephone company and the time to clear those problems (in minutes) Central Office (1) Time to clear problems (minutes) 2.52 0.78 0.93 1.02 1.48 1.60 1.75 2.97 3.93 5.45 0.53 0.80 0.97 1.05 1.48 1.60 2.85 3.10 4.15 6.32 Central Office (2) Time to clear problems (minutes) 0.08 0.52 0.60 0.65 1.10 1.53 1.92 3.30 3.75 2.23 0.10 0.58 0.60 0.72 1.48 1.65 2.10 3.75 4.02 7.55 (a) (8 marks) Based upon groupings of 1 minute intervals use EXCEL to obtain a histogram for each central office location (b) (6 marks) Prepare a full Descriptive Statistics profile, including Quartile 1 and Quartile 3, for each central office location. Explain how you prepared your results (c) (4 marks) Based on the histograms in (a), briefly describe the shape (symmetry, modality) of the data for each central office location. Do outliers exist in the data sets? Show how you know. (d) (4 marks) Which measures of location and dispersion should you use to describe the data for each central office location? What are their values? Give a brief explanation of the reason for your choice. (e) (4 marks) On the basis of your results of (a)-(d), are there any differences between the two central offices? Justify your answer carefully

Answer 1

a) You need to the Analysis ToolPak add-in to make histograms in excel. This can be done from File -> Options -> Add-Ins -> select Go from the Manage excel Add-ins option -> select Analysis ToolPak.

Then select Data -> Data Analysis -> histograms, and enter the desired range of data of input and bins. This gives you the histograms.

b) Descriptive statistics profile for Office 1:

Mean - obtained by averaging all data values - 2.05

Median - On arranging the data in ascending order, the data point lying in the mid of the distribution - 1.6

1st quartile - Median of the values ranging from the smallest value to the median of the entire data - 0.995

3rd quartile - Median of the values ranging from the median to the largest value - 3.035