In: Statistics and Probability
A magazine provided overall customer satisfaction scores for AT&T, Sprint, T-Mobile, and Verizon cell-phone services in major metropolitan areas throughout the United States. The rating for each service reflects the overall customer satisfaction considering a variety of factors such as cost, connectivity problems, dropped calls, static interference, and customer support. A satisfaction scale from 0 to 100 was used with indicating 0 completely dissatisfied and 100 indicating completely satisfied. The ratings for the four cell-phone services in 20 metropolitan areas are as shown.
| Metropolitan Area | AT&T | Sprint | T-Mobile | Verizon | 
|---|---|---|---|---|
| Atlanta | 70 | 63 | 77 | 80 | 
| Boston | 69 | 61 | 80 | 77 | 
| Chicago | 71 | 62 | 76 | 78 | 
| Dallas | 75 | 62 | 80 | 79 | 
| Denver | 71 | 64 | 79 | 78 | 
| Detroit | 73 | 62 | 83 | 80 | 
| Jacksonville | 73 | 61 | 81 | 82 | 
| Las Vegas | 72 | 65 | 80 | 82 | 
| Los Angeles | 66 | 62 | 74 | 79 | 
| Miami | 68 | 66 | 79 | 81 | 
| Minneapolis | 68 | 63 | 81 | 78 | 
| Philadelphia | 72 | 63 | 77 | 79 | 
| Phoenix | 68 | 63 | 82 | 82 | 
| San Antonio | 75 | 62 | 81 | 81 | 
| San Diego | 69 | 65 | 78 | 80 | 
| San Francisco | 66 | 66 | 79 | 76 | 
| Seattle | 68 | 64 | 80 | 78 | 
| St. Louis | 74 | 63 | 80 | 80 | 
| Tampa | 73 | 60 | 79 | 80 | 
| Washington | 72 | 65 | 77 | 77 | 
a. Consider T-Mobile first. What is the median rating (to 1 decimal)?
b. Develop a five-number summary for the T-Mobile service.
| Smallest value | |
| First quartile (to 2 decimals) | |
| Median (to 1 decimal) | |
| Third quartile (to 2 decimals) | |
| Largest value | 
c. Are there outliers for T-Mobile? Explain.
All ratings are between and .
- Select your answer -Yes, the data contain outliersNo, the data do not contain outliersItem 9
d. Repeat parts (b) and (c) for the other three cell-phone services.
| AT&T | Sprint | Verizon | |
| Smallest value | |||
| First quartile (to 2 decimals) | |||
| Median (to 1 decimal) | |||
| Third quartile (to 2 decimals) | |||
| Largest value | 
Are there outliers for AT&T? Explain.
Limits for AT&T(to 1 decimal) and
- Select your answer -Yes, the data contain outliersNo, the data do not contain outliersItem 27
Are there outliers for Sprint? Explain.
Limits for Sprint(to 2 decimals) and
- Select your answer -Yes, the data contain outliersNo, the data do not contain outliersItem 30
Are there outliers for Verizon? Explain.
Limits for Verizon(to 2 decimals) and
- Select your answer -Yes, the data contain outliersNo, the data do not contain outliersItem 33
e. Which of the following box plots accurately displays the data set?
| #1 | #2 | ||
| #3 | #4 | 
- Select your answer -Box plot #1Box plot #2Box plot #3Box plot #4Item 34
Which service did the magazine recommend as being best in terms of overall customer satisfaction?
- Select your answer -AT&TSprintT-MobileVerizonItem 35
Discuss what a comparison of the box plots tells about the four services.
- Select your answer -AT&T’sSprint’sT-Mobile’sVerizon’sItem 36 lowest rating is better than the highest - Select your answer -AT&T and SprintAT&T and VerizonSprint and VerizonT-Mobile and VerizonItem 37 ratings and is better than of the - Select your answer -AT&TSprintT-MobileVerizonItem 38 ratings. - Select your answer -AT&TSprintT-MobileVerizonItem 39 shows the lowest customer satisfaction ratings among the four services.
Note : Answer the first four question.
Five number summary AT&T


Five number summary Sprint  


Five number summary T-Mobile  


Five number summary Verizon

