Item 5 Mini Practice Set Responses
 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 Paper This response indicates little application of a reasonable strategy. Both the mean (8) and the median (3.5) are correct. Although the student defines the mean (the average) and the median (the middle number), the choice of mean to represent the fishes' typical weight demonstrates an incorrect application of this knowledge. The justification (the median only shows the middle number in the data, which doesn't really prove anything about a typical fish weight) shows a flaw in reasoning. The effect of the outlier on the mean is not considered. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.) Score Level 3 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 and provides a logically sound justification. (He only had one fish over 8 pounds. The median is a closer weight to the majority of the fish he caught.) This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 3 anchor paper.) Score Level 2 Paper This response indicates incomplete application of a reasonable strategy. While the mean (8) is correct, the median (3) is incorrect. The median is correctly chosen to represent the fishes' typical weight. Clearly presented justification is given (because the mean is too high because of the one 32 pound fish). This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)

Mini Practice Set 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 Paper This response indicates little application of a reasonable strategy. Both the mean (8) and the median (3.5) are correct. Although the student defines the mean (the average) and the median (the middle number), the choice of mean to represent the fishes' typical weight demonstrates an incorrect application of this knowledge. The justification (the median only shows the middle number in the data, which doesn't really prove anything about a typical fish weight) shows a flaw in reasoning. The effect of the outlier on the mean is not considered. This response demonstrates a minimal understanding and analysis of the problem. (Compare to this Level 1 anchor paper.)

 Score Level 3 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 and provides a logically sound justification. (He only had one fish over 8 pounds. The median is a closer weight to the majority of the fish he caught.) This response demonstrates a complete understanding and analysis of the problem. (Compare to this Level 3 anchor paper.)

 Score Level 2 Paper This response indicates incomplete application of a reasonable strategy. While the mean (8) is correct, the median (3) is incorrect. The median is correctly chosen to represent the fishes' typical weight. Clearly presented justification is given (because the mean is too high because of the one 32 pound fish). This response demonstrates a conceptual understanding and analysis of the problem. (Compare to this Level 2 anchor paper.)