Item 28 Anchor Papers    

HSA 2006 Algebra/Data Analysis Item 28

CID
CIDc7d980ef3a93e42584da57bf9f463cf6
itemNum
28
initialLetter
itemType
BCR
itemAnswerKey
N/A
itemMaxScorePoints
3
origNum
x

The student government wants to determine if students get better grades in morning or afternoon classes. They randomly surveyed 20 students that take math class in the morning and 20 students that take math class in the afternoon. The survey results are shown in the stem-and-leaf plots below.

Complete the following in the Answer Book:

  • What are the mean, median, and mode for each class?
  • Based on the data, do students get better grades in the morning classes? Use measures of central tendency to justify your answer.

Score Level 1 Anchor Paper

 

This response indicates little attempt to apply a reasonable strategy. The means for both the morning and afternoon classes are correct. The medians are incorrect because two answers are given for each median instead of one averaged answer (81 and 83; 76 and 79). The modes are incorrect (45; 35). The student indicates that the morning classes get better grades, but the justification using a measure of central tendency is missing (This is not clinicly proven; I would guess that they do better in the morning). The response demonstrates a minimal understanding and analysis of the problem.

image of student response

Score Level 1 Anchor Paper

 

This response indicates little attempt to apply a reasonable strategy. The modes for both the morning and afternoon classes are correct. However, the means and medians are all incorrect. The justification for students in the morning classes getting better grades is missing. The response demonstrates a minimal understanding and analysis of the problem.

image of student response

Score Level 2 Anchor Paper

 

This response indicates an incomplete application of a reasonable strategy. The median and mode are correct for the morning classes but the mean is incorrect. For the afternoon classes, the mode is correct but the mean and median are incorrect. The justification (according to the mean (81.2) and median (82) of the first class, they ranked higher than the second class (72.15 and 79)) supports the solution that the morning classes get better grades. Although some of the values used in the justification are incorrect, the relationship between the values still supports the solution. The response demonstrates a conceptual understanding and analysis of the problem.

image of student response

Score Level 2 Anchor Paper

 

This response indicates an incomplete application of a reasonable strategy. All the values given for the means, medians, and modes are correct. The justification for students getting better grades in the morning classes is missing. The response demonstrates a conceptual understanding and analysis of the problem.

image of student response

Score Level 2 Anchor Paper

 

This response indicates an incomplete application of a reasonable strategy. With the exception of the morning median, all the values given are correct. The justification (the average was higher in the morning classes) supports the solution that students get better grades in the morning. The response demonstrates a conceptual understanding and analysis of the problem.

image of student response

Score Level 3 Anchor Paper

 

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. All the values given for the means, medians and modes are correct. The justification (the morning class mean was 85 and the median was 82 while the afternoon class mean was 77.5 and median was 79) is fully developed and supports the solution that the morning classes get better grades. In addition, the student also justifies why the mode being higher in the afternoon classes does not mean that the afternoon classes get better grades. The response demonstrates a complete understanding and analysis of the problem.

image of student response

Score Level 3 Anchor Paper

 

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. All the values given for the means, medians and modes are correct. The justification (the mean for the morning class is 9.55 better than the afternoon classes; the median is 4.5 better) is fully developed and supports the solution that the morning classes get better grades. The response demonstrates a complete understanding and analysis of the problem.

image of student response

Score Level 3 Anchor Paper

 

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. All the values given for the means, medians and modes are correct. The justification (the mean and median are higher but the mode is lower) is fully developed and supports the solution that the morning classes get better grades. The response demonstrates a complete understanding and analysis of the problem.

image of student response
 

Anchor Papers ~ Algebra/Data Analysis ~ Item 28

HSA 2006 Algebra/Data Analysis Item 28

CID
CIDc7d980ef3a93e42584da57bf9f463cf6
itemNum
28
initialLetter
itemType
BCR
itemAnswerKey
N/A
itemMaxScorePoints
3
origNum
x

The student government wants to determine if students get better grades in morning or afternoon classes. They randomly surveyed 20 students that take math class in the morning and 20 students that take math class in the afternoon. The survey results are shown in the stem-and-leaf plots below.

Complete the following in the Answer Book:

  • What are the mean, median, and mode for each class?
  • Based on the data, do students get better grades in the morning classes? Use measures of central tendency to justify your answer.

 

Score Level 1 Anchor Paper

 

This response indicates little attempt to apply a reasonable strategy. The means for both the morning and afternoon classes are correct. The medians are incorrect because two answers are given for each median instead of one averaged answer (81 and 83; 76 and 79). The modes are incorrect (45; 35). The student indicates that the morning classes get better grades, but the justification using a measure of central tendency is missing (This is not clinicly proven; I would guess that they do better in the morning). The response demonstrates a minimal understanding and analysis of the problem.

image of student response

 

Score Level 1 Anchor Paper

 

This response indicates little attempt to apply a reasonable strategy. The modes for both the morning and afternoon classes are correct. However, the means and medians are all incorrect. The justification for students in the morning classes getting better grades is missing. The response demonstrates a minimal understanding and analysis of the problem.

image of student response

 

Score Level 2 Anchor Paper

 

This response indicates an incomplete application of a reasonable strategy. The median and mode are correct for the morning classes but the mean is incorrect. For the afternoon classes, the mode is correct but the mean and median are incorrect. The justification (according to the mean (81.2) and median (82) of the first class, they ranked higher than the second class (72.15 and 79)) supports the solution that the morning classes get better grades. Although some of the values used in the justification are incorrect, the relationship between the values still supports the solution. The response demonstrates a conceptual understanding and analysis of the problem.

image of student response

 

Score Level 2 Anchor Paper

 

This response indicates an incomplete application of a reasonable strategy. All the values given for the means, medians, and modes are correct. The justification for students getting better grades in the morning classes is missing. The response demonstrates a conceptual understanding and analysis of the problem.

image of student response

 

Score Level 2 Anchor Paper

 

This response indicates an incomplete application of a reasonable strategy. With the exception of the morning median, all the values given are correct. The justification (the average was higher in the morning classes) supports the solution that students get better grades in the morning. The response demonstrates a conceptual understanding and analysis of the problem.

image of student response

 

Score Level 3 Anchor Paper

 

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. All the values given for the means, medians and modes are correct. The justification (the morning class mean was 85 and the median was 82 while the afternoon class mean was 77.5 and median was 79) is fully developed and supports the solution that the morning classes get better grades. In addition, the student also justifies why the mode being higher in the afternoon classes does not mean that the afternoon classes get better grades. The response demonstrates a complete understanding and analysis of the problem.

image of student response

 

Score Level 3 Anchor Paper

 

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. All the values given for the means, medians and modes are correct. The justification (the mean for the morning class is 9.55 better than the afternoon classes; the median is 4.5 better) is fully developed and supports the solution that the morning classes get better grades. The response demonstrates a complete understanding and analysis of the problem.

image of student response

 

Score Level 3 Anchor Paper

 

This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. All the values given for the means, medians and modes are correct. The justification (the mean and median are higher but the mode is lower) is fully developed and supports the solution that the morning classes get better grades. The response demonstrates a complete understanding and analysis of the problem.

image of student response