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The task asks students to compare two ambulance companies on the basis of their timely response to Emergency 911 dispatches. Students must use appropriate graphs or measures of center and spread or both to present a persuasive argument for choosing one of the ambulance companies over the other.
Materials: Graph paper
Estimated time: 60 minutes
Last week there was an accident at the Waterfront Amusement Park in Bay City. A seat on one of the rides broke loose resulting in the death of two teenagers. The owners of the amusement park have charged that if ambulances had responded more quickly, the two teens would have survived. They have threatened to sue the Bay City 911 emergency service for failing to dispatch ambulances efficiently.
The Bay City Council has hired your firm to conduct an independent investigation of the City's 911 response. Upon completion of your investigation, you are to make a report to the City Council on your findings along with any recommendations for improving the 911 emergency service in the neighborhood of the amusement park.
You start to work on this assignment. Your investigation has uncovered the following information.
Based on the information above and your analysis of the response time data, you conclude that the Bay City Council needs to establish a policy about which service to call.
Write a report to the Bay City Council advising them of your recommendations about which service the 911 operators should dispatch in the area around the amusement park.
You will need to prepare charts, graphs, calculations or other materials to include in your report to support your recommendations.
Be sure to give clear reasons for the policy you are recommending.
Date
|
Time
|
Company
|
Response
Time
|
| of
Call
|
of
Call
|
Name
|
in
minutes
|
| Wed.,
May 1
|
2:20
AM
|
Arrow
|
11
|
| Wed.,
May 1
|
12:41
PM
|
Arrow
|
8
|
| Wed.,
May 1
|
2:29
PM
|
Metro
|
11
|
| Thurs.,
May 2
|
8:14
AM
|
Metro
|
8
|
| Thurs.,
May 2
|
6:23
PM
|
Metro
|
16
|
| Fri.,
May 3
|
4:15
AM
|
Metro
|
7
|
| Fri.,
May 3
|
8:41
AM
|
Arrow
|
19
|
| Sat.,
May 4
|
7:12
AM
|
Metro
|
11
|
| Sat.,
May 4
|
7:43
PM
|
Metro
|
11
|
| Sat.,
May 4
|
10:02
PM
|
Arrow
|
7
|
| Sun.,
May 5
|
12:22
PM
|
Metro
|
12
|
| Mon.,
May 6
|
6:47
AM
|
Metro
|
9
|
| Mon.,
May 6
|
7:15
AM
|
Arrow
|
16
|
| Mon.,
May 6
|
6:10
PM
|
Arrow
|
8
|
| Tues.,
May 7
|
5:37
PM
|
Metro
|
16
|
| Tues.,
May 7
|
9:37
PM
|
Metro
|
11
|
| Thurs.,
May 9
|
5:30
AM
|
Arrow
|
17
|
| Thurs.,
May 9
|
6:18
PM
|
Arrow
|
6
|
| Fri.,
May 10
|
6:25
AM
|
Arrow
|
16
|
| Sat.,
May 11
|
1:03
AM
|
Metro
|
12
|
| Mon.,
May 13
|
6:40
AM
|
Arrow
|
17
|
| Mon.,
May 13
|
3:25
PM
|
Metro
|
15
|
| Tues.,
May 14
|
4:59
PM
|
Metro
|
14
|
| Thurs.,
May 16
|
10:11
AM
|
Metro
|
8
|
| Thurs.,
May 16
|
11:45
AM
|
Metro
|
10
|
| Fri.,
May 17
|
11:09
AM
|
Arrow
|
7
|
| Fri.,
May 17
|
9:15
PM
|
Arrow
|
8
|
| Fri.,
May 17
|
11:15
PM
|
Metro
|
8
|
| Mon.,
May 20
|
7:25
AM
|
Arrow
|
17
|
| Mon.,
May 20
|
4:20
PM
|
Metro
|
19
|
| Thurs.,
May 23
|
2:39
PM
|
Arrow
|
10
|
| Thurs.,
May 23
|
3:44
PM
|
Metro
|
14
|
| Fri.,
May 24
|
8:56
PM
|
Metro
|
10
|
| Sat.,
May 25
|
8:30
PM
|
Arrow
|
8
|
| Sun.,
May 26
|
6:33
AM
|
Metro
|
6
|
| Mon.,
May 27
|
4:21
PM
|
Arrow
|
9
|
| Tues.,
May 28
|
8:07
AM
|
Arrow
|
15
|
| Tues.,
May 28
|
5:02
PM
|
Arrow
|
7
|
| Wed.,
May 29
|
10:51
AM
|
Metro
|
9
|
| Wed.,
May 29
|
5:11
PM
|
Metro
|
18
|
| Thurs.,
May 30
|
4:16
AM
|
Arrow
|
10
|
| Fri.,
May 31
|
8:59
AM
|
Metro
|
11
|
Calculating mean response times for each ambulance service is a reasonable start to analyzing the data. However, the mean response time for Arrow Ambulance Service is 11.36 minutes. The mean response time for Metro Ambulances is 11.56 minutes. The difference of .2 minute is not significant and suggests some further investigation of the data is warranted.
A likely choice would be to select response time and time of call to see if there is a relationship between these variables. A scatter plot graphing the response times for given times at which the calls were placed is an appropriate graphical representation.
An analysis of the scatter plot suggests that Metro Ambulances tends to have a quicker response time during the a.m. hours and Arrow Ambulance Service tends to have a quicker response time during the p.m. hours. Given this further analysis, a reasonable policy recommendation would be to have 911 operators dispatch Metro Ambulances between the morning hours of 12 midnight until 12 noon and to dispatch Arrow Ambulance Service during the afternoon and evening hours of 12 noon until 12 midnight.
A more complete solution would take into account whether there might be other relationships that might affect a policy recommendation. Further analysis of the data could consider the relationship between response time and the day of the week in which a call is recorded. A scatterplot of these data are presented next.
An analysis of this scatterplot suggests that the day of the week in which a call is received by a 911 operator has no effect on the response time.
Read through the task with students, making sure they understand the context of the task. You might ask some questions to check their understanding, such as:
What is a 911 service?
Could someone explain what a log sheet is?
What does the data in the log sheet represent?
What does it mean in the problem when it refers to "response time"?
After you are sure that students understand the context and what they are to do, leave them to their work. DO NOT give hints on how to analyze the data; students are to choose their own methods.
To be able to tackle this task, students in the middle grades will need to have had some experiences with situations that involve selecting appropriate variables to sort data. We have found that without this kind of experience, students do not make much progress beyond simply calculating the mean response times, or constructing graphs that are not reasonable (e.g., circle graphs) or informative, or constructing graphs using variables that are not salient.
This section offers a characterization of student responses and provides indications of the ways in which the students were successful or unsuccessful in engaging with and completing the task. The descriptions are keyed to the Core Elements of Performance. Our global descriptions of student work range from "The student needs significant instruction" to " The student's work meets the essential demands of the task." Samples of student work that exemplify these descriptions of performance are included below, accompanied by commentary on central aspects of each student's response. These sample responses are representative; they may not mirror the global description of performance in all respects, being weaker in some and stronger in others.
The characterization of student responses for this task is based on these 'Core Elements of Performance':
Students calculate a single statistic (e.g., mean or median response time). They recommend one ambulance service over the other on the basis of a comparison of this single statistic even though the mean difference is only .2 minute, not significant for making a policy recommendation. The analysis of the data ignores all other variables except response time.
Student A
This group calculates the mean response time for Metro and Arrow ambulance services and then recommends that Metro is the best choice because their response time (incorrectly calculated) is .35 minutes quicker. The presentation of a bar graph of the mean response times adds nothing to the persuasiveness of their argument.
Students may calculate measures of center and explore the data with other kinds of analysis (e.g., box plots, stem and leaf plots) but they consider only a single variable - the response times of the two ambulance services. They demonstrate some ability to use their statistical "toolkit" but the analysis is not connected to the real-world context of the problem and the argument is weak.
Student B
This group restricts its analysis to a single variable - response time. They construct stem and leaf plots and box plots but use these displays to make a rather weak argument. They base their response on differences in the distribution of the response times, claiming that Arrow's times are more spread out. This group has not carefully and thoroughly interrogated the data and their argument is not persuasive.
Students select appropriate variables for analyzing the data (e.g., response time in relation to time of call), make appropriate calculations, use appropriate graphical representations, and make a reasonable recommendation based on their analysis. There may be errors in the calculations and in the graphs. However, students do not fully interrogate the data set, thereby not ruling out other possible salient relationships (e.g., response time in relation to day of the call). The recommendations follow from the analysis but the report may lack clarity and thoroughness.
Student C
These students have selected the response time and the time of the call and have used a scatterplot to represent their analysis. They have not selected a scale that allows them to present the entire data set on one side of the paper, thereby making it difficult to interpret their graph. Their recommendation is reasonable given the way in which they have analyzed the data. They have not pursued any other relationships among the variables in the data set.
Students select appropriate variables for sorting, analyzing and representing the data. Students consider a number of relationships and use a variety of analytic tools to fully interrogate the data set. Their recommendations follow from and are supported by their analysis of the data.
Student D
These students first considered the relationship between the response time and the time of the call, and drew a broken line graph. Although it is not appropriate to connect the points on this graph given the context of the problem, the students have presented a visually powerful representation of the data, one that supports a recommendation to use Metro in the a.m. and Arrow in the p.m. However, these students went on to interrogate the data further. They drew from their statistical "toolkit," constructing a box plot, line plot, 5-number summary and individual graphs for each ambulance service but concluded that this further analysis did not add anything new to their original analysis.
Student E
These students analyzed two relationships - of response time to time of call, and response time to day of the call. They concluded that there was a relationship between time of call and response time and recommended that Metro be called in the a.m. and Arrow in the p.m. They also commented that the day of the week did not seem to have an effect on the response time. These students have done a careful interrogation of the data and have made recommendations that follow from and are supported by their analysis.
This assessment package was designed and developed by members of the Balanced Assessment Project team, particularly Judith Zawojewski, Mary Bouck, John Gillespie, Sandra Wilcox, Helene Alpert, Angela Krebs, Faaiz Gierdien, Whitney Johnson and Kyle Ward. The editor was Mary Bouck.
Many others have made helpful comments and suggestions in the course of the development. We thank them all. The project is particularly grateful to the mathematics consultants, teachers and students with whom these tasks were developed and tested, particularly Josh Coty, Ray Fauch, Julie Faulkner, Loraine Gawlik, Yvonne Grant, Lisa Harden, Liz Jones, Terri Keusch, Tom Little, Tammy McCarthy, Jan Palkowski, Marlene Robinson, Mark Rudd, Nancy Rudd, Mary Beth Schmitt, Janet Small, Judy Van Der Meullen, Patti Wagner, and Mike Wilson.
The project was directed by Alan Schoenfeld, Hugh Burkhardt, Phil Daro, Jim Ridgway, Judah Schwartz and Sandra Wilcox.
The package consists of materials compiled or adapted from work done at the four sites of the Balanced Assessment Project.
The work of this project was supported by a grant from the National Science Foundation. The opinions expressed in these materials do not necessarily represent the position, policy, or endorsement of the Foundation.
Copyright (c) 1995 Regents of the University of California. All rights reserved.
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Page updated 4 March 1998 For further information please contact wilcoxs@pilot.msu.edu |
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