Item 5 Anchor Papers
 Matt caught 6 fish and recorded each of their weights as shown in the table below. Complete the following in the Answer Book: Find the mean and the median of the data.  Which measure of central tendency, mean or median, should Matt use to best represent the typical weight of the fish he caught? Use mathematics to justify your answer.

 Score Level 1 Anchor Paper This response indicates little application of a reasonable strategy. The mean (8) is correct, but the median (3) is incorrect. The student incorrectly chooses the mean to represent the fishes' typical weight. Although the student correctly defines the mean (the average weight of the fish), the justification contains a flaw in reasoning (the average allows people to see what the majority of fish weigh). The effect of the outlier on the mean is not considered. This response demonstrates a minimal understanding and analysis of the problem. Score Level 1 Anchor Paper This response indicates little application of a reasonable strategy. Both the mean (8) and the median (3.5) are correct. The student defines the mean (the amount in the middle, average weight) and the median (the middle of the data), which indicates that the student does not have a clear understanding of the mean and median. The student incorrectly chooses the mean to represent the fishes' typical weight. The effect of the outlier on the mean is not considered. This response demonstrates a minimal understanding and analysis of the problem. Score Level 1 Anchor Paper This response indicates little application of a reasonable strategy. The mean (8) and the median (3.5) are correct. The student correctly chooses the median to represent the fishes' typical weight; however, no justification is given. This response demonstrates a minimal understanding and analysis of the problem. Score Level 2 Anchor Paper This response indicates incomplete application of a reasonable strategy. While the mean (8) is correct, the median (4) is incorrect. The student correctly selects the median to represent the fishes' typical weight. Complete justification is provided. (He caught one fish that was much heavier than the rest. It was 32 pounds and was an outlier. This weight brought the mean up to a higher number. Most of the fish he caught were 2, 3, 4, and 5 pounds) This response demonstrates a conceptual understanding and analysis of the problem. Score Level 2 Anchor Paper This response indicates incomplete application of a reasonable strategy. The mean (8) is correct, but the median (4) is incorrect. The student correctly chooses the median to represent the fishes' typical weight. The justification (because there is an outlier of 32. This makes the mean greater than what it should be) supports the solution. This 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. Both the mean (8) and the median (3.5) are correct. The student correctly selects the median to represent the fishes' typical weight. A clearly presented justification that supports the solution is given. (The median was not affected by the outlier, which was 32 pounds. The mean, on the other hand, was affected by the outlier and as a result brought the average weight up.) This 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 (8) and the median (3.5) are correct. The median is chosen to represent the fishes' typical weight. The justification (because 5 out of the 6 fish are 2-5 pounds. The 32-pound fish throws off the mean because it is so much higher) is logically sound and supports the solution. This response demonstrates a complete understanding and analysis of the problem.

Anchor Papers ~ Algebra/Data Analysis ~ Item 5

 Matt caught 6 fish and recorded each of their weights as shown in the table below. Complete the following in the Answer Book: Find the mean and the median of the data.  Which measure of central tendency, mean or median, should Matt use to best represent the typical weight of the fish he caught? Use mathematics to justify your answer.

 Score Level 1 Anchor Paper This response indicates little application of a reasonable strategy. The mean (8) is correct, but the median (3) is incorrect. The student incorrectly chooses the mean to represent the fishes' typical weight. Although the student correctly defines the mean (the average weight of the fish), the justification contains a flaw in reasoning (the average allows people to see what the majority of fish weigh). The effect of the outlier on the mean is not considered. This response demonstrates a minimal understanding and analysis of the problem.

 Score Level 1 Anchor Paper This response indicates little application of a reasonable strategy. Both the mean (8) and the median (3.5) are correct. The student defines the mean (the amount in the middle, average weight) and the median (the middle of the data), which indicates that the student does not have a clear understanding of the mean and median. The student incorrectly chooses the mean to represent the fishes' typical weight. The effect of the outlier on the mean is not considered. This response demonstrates a minimal understanding and analysis of the problem.

 Score Level 1 Anchor Paper This response indicates little application of a reasonable strategy. The mean (8) and the median (3.5) are correct. The student correctly chooses the median to represent the fishes' typical weight; however, no justification is given. This response demonstrates a minimal understanding and analysis of the problem.

 Score Level 2 Anchor Paper This response indicates incomplete application of a reasonable strategy. While the mean (8) is correct, the median (4) is incorrect. The student correctly selects the median to represent the fishes' typical weight. Complete justification is provided. (He caught one fish that was much heavier than the rest. It was 32 pounds and was an outlier. This weight brought the mean up to a higher number. Most of the fish he caught were 2, 3, 4, and 5 pounds) This response demonstrates a conceptual understanding and analysis of the problem.

 Score Level 2 Anchor Paper This response indicates incomplete application of a reasonable strategy. The mean (8) is correct, but the median (4) is incorrect. The student correctly chooses the median to represent the fishes' typical weight. The justification (because there is an outlier of 32. This makes the mean greater than what it should be) supports the solution. This 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. Both the mean (8) and the median (3.5) are correct. The student correctly selects the median to represent the fishes' typical weight. A clearly presented justification that supports the solution is given. (The median was not affected by the outlier, which was 32 pounds. The mean, on the other hand, was affected by the outlier and as a result brought the average weight up.) This 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 (8) and the median (3.5) are correct. The median is chosen to represent the fishes' typical weight. The justification (because 5 out of the 6 fish are 2-5 pounds. The 32-pound fish throws off the mean because it is so much higher) is logically sound and supports the solution. This response demonstrates a complete understanding and analysis of the problem.