Question

Speedy Swift is a package delivery service that serves the greater Atlanta, Georgia, metropolitan area. To maintain customer loyalty, one of Speedy Swift's performance objectives is on-time delivery. To monitor its performance, each delivery is measured on the following scale: early (package delivered before the promised time), on-time (package delivered within 15 minutes of the promised time), late (package delivered more than 15 minutes past the promised time), or lost (package never delivered). Speedy Swift's objective is to deliver 99% of all packages either early or on-time. Another objective is to never lose a package.

On-time On-time Early Late On-time On-time On-time On-time Late On-time
Early On-time On-time Early On-time On-time On-time On-time On-time On-time
Early On-time Early On-time On-time On-time Early On-time On-time On-time
Early On-time On-time Late Early Early On-time On-time On-time Early
On-time Late Late On-time On-time On-time On-time On-time On-time On-time
On-time Late Early On-time Early On-time Lost On-time On-time On-time
Early Early On-time On-time Late Early Lost On-time On-time On-time
On-time On-time Early On-time Early On-time Early On-time Late On-time
On-time Early On-time On-time On-time Late On-time

Required:
a. What scale is used to measure delivery performance? What kind of variable is delivery performance?
b. Construct a frequency table for delivery performance for last month.
c. Construct a relative frequency table for delivery performance last month.
d. Construct a bar chart of the frequency table for delivery performance for last month.
e. Construct a pie chart of on-time delivery performance for last month.
f. Analyze the data summaries and write an evaluation of last month's delivery performance as it relates to Speedy Swift's performance objectives. Write a general recommendation for further analysis.

Answer 1

See Explanation and attachments

Explanation:

Given

See question for data

Solving (a):

The scale used is an ordinal scale.

Ordinals scale uses hierarchy arrangement and the data can be arranged as:

`EARLY ->> ON-TIME ->> LATE ->> LOST`

The variable of the delivery performance is qualitative because it is non-numerical

Solving (b): Frequency table

From the table, we have:

`On - Time = 57`
`Early = 19`
`Late = 9`
`Lost = 2`

So, the frequency distribution table is:

`\begin{array}{cc}{Performance}&{Frequency}&{On-Time}&{57}&{Early}&{19}&{Late}&{9} & {Loss} & {2} & {Total} & {87}\end{array}`

Solving (c): Frequency table.

To do this, we add another column (Relative Frequency) to the above table.

The relative frequency is calculated as:

`Relative\ Frequency = (Frequency)/(Total)`

So, we have:

`On - Time = (57)/(87) = 0.656`
`Early = (19)/(87) = 0.218`

`Late = (9)/(87) = 0.103`
`Lost = (2)/(87) = 0.023`

So, the frequency distribution table is:

`\begin{array}{ccc}{Performance}&{Frequency}&{Relative\ Frequency} & {On-Time}&{57}&{0.656}&{Early}&{19}&{0.218} & {Late}&{9} & {0.103} & {Loss} & {2} & {0.023} & {Total} & {87}&{1}\end{array}`

Solving (d & e): See attachment 1 for bar chart & attachment 2 for pie chart

Solving (f):

From the question, we understand that the object is to return 99% early or on time and never to lose a package.

The analysis is as follows:

Early and On-Time (ET) packages

`ET = (Early + On-Time)/(Total) * 100\%`

`ET = (57 + 19)/(87) * 100\%`

`ET = (76)/(87) * 100\%`

`ET = (7600)/(87) \%`

`ET = 87.4 \%`

Lost packages

`Lost = (Lost)/(Total) * 100\%`

`Lost = (2)/(87) * 100\%`

`Lost = (200)/(87) \%`

`Lost = 2.30\%`

From the above analysis, we can see that 87.4% of the packages were delivered early enough and 2.30% were lost.

The fraction of packages delivered early can be improved and the fraction of lost packages can be reduced by exploring the chances of taking alternative routes when possible.