
	Item 22 Anchor Papers

HSA 2008 Algebra/Data Analysis Item 22

CID: CIDfce1cb001c4f8394c06ced6735e9c24a
itemNum: 22
initialLetter
itemType: BCR
itemAnswerKey: N/A
itemMaxScorePoints: 3
origNum: 6

Nineteen families live in a small town. The income for each family is listed in the table below.

Complete the following in the Answer Book:

What are the median and mean family incomes for this small town?
Should the mean or median be used to describe the typical family income in this small town? Use mathematics to justify your answer.
If each family’s income increases by $1,000, Alison believes the mean family income will increase more than the median family income. Do you agree with Alison? Use mathematics to justify your answer.

Score Level 1 Anchor Paper
This response indicates little attempt to apply a reasonable strategy. The mean and the median are both incorrect. The student correctly selects the median to describe the typical family income in the town and gives justification (there is a large income that will throu off the mean by alot). No correct justification is given for disagreeing with Alison’s belief that the mean will increase more than the median if each family’s income increases by $1000. The response demonstrates a minimal understanding and analysis of the problem.
Score Level 1 Anchor Paper
This response indicates little attempt to apply a reasonable strategy. The mean and the median are both correct. The student incorrectly selects the mean to describe the typical family income in the town and no correct justification is given. The student incorrectly states that Alison is correct in her belief that the mean will increase more than the median if each family’s income increases by $1000. No valid justification is given. The response demonstrates a minimal understanding and analysis of the problem.
Score Level 2 Anchor Paper
This response indicates an incomplete application of a reasonable strategy. The mean and the median are both correct. The student correctly selects the median to describe the typical family income in the town and gives justification ($320,000 is only made by one of the nineteen families and $320,000 is an outlier). Although the student correctly disagrees with Alison’s belief that the mean will change more than the median if each family’s income increases by $1000, no correct justification is given. The response demonstrates a conceptual understanding and analysis of the problem.
Score Level 2 Anchor Paper
This response indicates an incomplete application of a reasonable strategy. The mean and the median are both correct. The student incorrectly selects the mean to describe the typical family income in the town and no correct justification is given. The student correctly disagrees with Alison’s belief that the mean will change more than the median if each family’s income increases by $1000 and gives justification (the mean income would be $57,578.94737 and the median would be $41,000 both the mean and the median would increase by the same amount). The response demonstrates a conceptual understanding and analysis of the problem.
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. The mean and the median are both correct. The student correctly selects the median to describe the typical family income in the town and gives justification (more than half (50%) of the families are making around $40,000. If we were to use the mean only one family would be able to say that they make $56,579 as an income). The student correctly disagrees with Alison’s belief that the mean will change more than the median if each family’s income increases by $1000 and gives justification (The mean and the median both changed by $1000. For example, the mean before: $56,579, mean now: $57,579. The median before: $40,000, the median now: $41,000). The response demonstrates a complete understanding and analysis of the problem.
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. The mean and the median are both correct. The student correctly selects the median to describe the typical family income in the town and gives justification (its centrally located in the data. The mean can’t be used because it’s affected by the outlier 320,000. The outlier mades it higher than most of the data in the table). The student correctly disagrees with Alison’s belief that the mean will change more than the median if each family’s income increases by $1000 and gives justification (the new mean would be $57579 and the new median would be $41000. The mean family income increase by $1000 and the median family income increase by $1000. They increase by the same amount). The response demonstrates a complete understanding and analysis of the problem.

Anchor Papers ~ Algebra/Data Analysis ~ Item 22

HSA 2008 Algebra/Data Analysis Item 22

CID: CIDfce1cb001c4f8394c06ced6735e9c24a
itemNum: 22
initialLetter
itemType: BCR
itemAnswerKey: N/A
itemMaxScorePoints: 3
origNum: 6

Nineteen families live in a small town. The income for each family is listed in the table below.

Complete the following in the Answer Book:

What are the median and mean family incomes for this small town?
Should the mean or median be used to describe the typical family income in this small town? Use mathematics to justify your answer.
If each family’s income increases by $1,000, Alison believes the mean family income will increase more than the median family income. Do you agree with Alison? Use mathematics to justify your answer.

Score Level 1 Anchor Paper

This response indicates little attempt to apply a reasonable strategy. The mean and the median are both incorrect. The student correctly selects the median to describe the typical family income in the town and gives justification (there is a large income that will throu off the mean by alot). No correct justification is given for disagreeing with Alison’s belief that the mean will increase more than the median if each family’s income increases by $1000. The response demonstrates a minimal understanding and analysis of the problem.

Score Level 1 Anchor Paper

This response indicates little attempt to apply a reasonable strategy. The mean and the median are both correct. The student incorrectly selects the mean to describe the typical family income in the town and no correct justification is given. The student incorrectly states that Alison is correct in her belief that the mean will increase more than the median if each family’s income increases by $1000. No valid justification is given. The response demonstrates a minimal understanding and analysis of the problem.

Score Level 2 Anchor Paper

This response indicates an incomplete application of a reasonable strategy. The mean and the median are both correct. The student correctly selects the median to describe the typical family income in the town and gives justification ($320,000 is only made by one of the nineteen families and $320,000 is an outlier). Although the student correctly disagrees with Alison’s belief that the mean will change more than the median if each family’s income increases by $1000, no correct justification is given. The response demonstrates a conceptual understanding and analysis of the problem.

Score Level 2 Anchor Paper

This response indicates an incomplete application of a reasonable strategy. The mean and the median are both correct. The student incorrectly selects the mean to describe the typical family income in the town and no correct justification is given. The student correctly disagrees with Alison’s belief that the mean will change more than the median if each family’s income increases by $1000 and gives justification (the mean income would be $57,578.94737 and the median would be $41,000 both the mean and the median would increase by the same amount). The response demonstrates a conceptual understanding and analysis of the problem.

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. The mean and the median are both correct. The student correctly selects the median to describe the typical family income in the town and gives justification (more than half (50%) of the families are making around $40,000. If we were to use the mean only one family would be able to say that they make $56,579 as an income). The student correctly disagrees with Alison’s belief that the mean will change more than the median if each family’s income increases by $1000 and gives justification (The mean and the median both changed by $1000. For example, the mean before: $56,579, mean now: $57,579. The median before: $40,000, the median now: $41,000). The response demonstrates a complete understanding and analysis of the problem.

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. The mean and the median are both correct. The student correctly selects the median to describe the typical family income in the town and gives justification (its centrally located in the data. The mean can’t be used because it’s affected by the outlier 320,000. The outlier mades it higher than most of the data in the table). The student correctly disagrees with Alison’s belief that the mean will change more than the median if each family’s income increases by $1000 and gives justification (the new mean would be $57579 and the new median would be $41000. The mean family income increase by $1000 and the median family income increase by $1000. They increase by the same amount). The response demonstrates a complete understanding and analysis of the problem.