The following 17 Sample Student Responses represent a range of score points.

Score for Sample Student Response #1: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. Both the means and the medians are correct, and the student correctly indicates that the means of the two sets of data could be used to support the conclusion. ("Sam could use the mean from both sets of data to show that the age of presidents has gone down.") The response correctly states that the data does not provide strong enough support to make the conclusion valid. The justification for this answer is clearly presented and fully developed. ("One reason is that the mean is less than 2 points away. Also the mean is larger in the first catagory; the median is larger in the second catagory.") This response demonstrates a complete understanding and analysis of the problem.

Score for Sample Student Response #2: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. Both means are correct, but the medians are missing. The student correctly indicates that the means could be used to support the conclusion. ("He could support his conclusion by stating that the average age of the presidents from 1789 to 1845 is 1.3 years greater than it was from 1945 to 2000.") The response correctly states that the data does not provide strong enough support to make the conclusion valid. To justify this answer, the student notes that even though the means have decreased, the change is too small to make the conclusion valid. ("Compared to an age of around 50 to 60 years old, a 1.3 year difference between the presidents of now and then, doesn't seem that big.") This response demonstrates a conceptual understanding and analysis of the problem.

Score for Sample Student Response #3: Rubric Score 1

Annotation: This response indicates little attempt to apply a reasonable strategy. The only correct answer ("58.1") is the mean for the presidents who served between 1789 and 1845. The mean for the presidents who served between 1945 and 2000 and both medians are incorrect. No attempt is made to describe how the data could support the conclusion. Although the student correctly states that the data does not provide strong enough support to make the conclusion valid, no relevant justification is given. This response demonstrates a minimal understanding and analysis of the problem.

Score for Sample Student Response #4: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. Both the means and the medians are correct, and the student correctly indicates that the means could be used to support the conclusion. ("He could show people the mean of the data from both sets and show that the age means went down.") Although the student correctly states that the data does not provide strong enough support to make the conclusion valid, the only justification given is that "he would need more support." Because this statement is unclear, the justification is incomplete. This response demonstrates a conceptual understanding and analysis of the problem.

Score for Sample Student Response #5: Rubric Score 1

Annotation: This response indicates little attempt to apply a reasonable strategy. The mean for the presidents who served between 1789 and 1845 is correct, but the median is incorrect. The correct answer is 57, not "56.5." Both the mean and the median for the presidents who served between 1945 and 2000 are correct. The answer for how the data could support the conclusion shows serious flaws in reasoning and does not give any relevant justification. The student incorrectly states that the data does provide support strong enough to make the conclusion valid. This response demonstrates a minimal understanding and analysis of the problem.

Score for Sample Student Response #6: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. Both the means and the medians are correct. The response correctly indicates that the means could be used to support the conclusion. ("Sam could use this data to support his conclusion by comparing the means. The mean for 1789 to 1845 decreased one compared to the mean from 1845 to 2000.") The student correctly states that the data does not provide strong enough support to make the conclusion valid. Justification that is logically sound and clearly presented also is given ("I don't think this data strongly supports Sam's theory because the medians of the two time periods was about the same. One year's difference isn't that much of a span anyway.") and indicates that the difference between the ages in the two different time periods is so small that it is not strong enough to support the conclusion. This response demonstrates a complete understanding and analysis of the problem.

Score for Sample Student Response #7: Rubric Score 1

Annotation: This response indicates little attempt to apply a reasonable strategy. Both the means and the medians are correct. The student states that "He could use this data to support his conclusion by finding the mean and median for 1789 to 2000." The mean of the given data does show a decrease, but the median shows an increase and, therefore, using both the mean and median would not support the conclusion. While the student indicates that the data "might not be strong enough to support his conclusion," no justification is given to support this answer. This response demonstrates a minimal understanding and analysis of the problem.

Score for Sample Student Response #8: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. Both the means and the medians are correct. The response correctly indicates that the means could be used to support the conclusion. ("If Sam wanted to show that the ages decreased he should use the mean and say that the more recent mean is lower than the older one.") Fully developed justification is given for the answer that the data does not provide strong enough support to make the conclusion valid ("only the mean is lower for the 1945-2000 presidents, and a lot of the ages are higher than the 1789-1845 presidents"). This justification clearly shows why the data is not strong enough to make the conclusion valid. This response demonstrates complete understanding and analysis of the problem.

Score for Sample Student Response #9: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. All four measures of central tendency are correct. The response correctly identifies the mean as supporting the conclusion. ("He could use the mean to show that the ages have decreased because the mean from 1789-1845 is greater than the mean from 1945-2000.") The student incorrectly tries to justify that the data is strong enough to make the conclusion valid. ("Yes I do think he does have strong enough data because the mean clearly shows that the ages have decreased.") Even though the means do show a decrease, the medians show an increase and, therefore, would not offer support strong enough to make the conclusion valid. This response demonstrates a conceptual understanding and analysis of the problem.

Score for Sample Student Response #10: Rubric Score 1

Annotation: This response indicates little attempt to apply a reasonable strategy. The means for both sets of data and the median for the presidents who served between 1945 and 2000 are correct. However, the median for the presidents who served between 1789 and 1845 is incorrect ("57.5" instead of 57). No attempt is made to answer the remainder of the question. This response demonstrates a minimal understanding and analysis of the problem.

Score for Sample Student Response #11: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. All four measures of central tendency are correct. The student correctly indicates that the means could be used to support the conclusion ("use the mean because it goes down by 1.3 years"). The response correctly states that the data does not provide strong enough support to make the conclusion valid. The justification given to support this answer is clearly presented. ("I don't think the data provides enough strong data to support his conclusion because the mean may go down but the median {middle age} goes up by one year, therefore causing a disagreement over if it's up or down.")

Score for Sample Student Response #12: Rubric Score 1

Annotation: This response indicates little attempt to apply a reasonable strategy. All four measures of central tendency are correct; however, the response to the second bullet does not describe how data could be used to support the conclusion. The student incorrectly states that the data is strong enough to make the conclusion valid. This response demonstrates a minimal understanding and analysis of the problem.

Score for Sample Student Response #13: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. Both the mean and the median are correct for the presidents who served between 1789 and 1845. The mean is correct for the presidents who served between 1945 and 2000, but the median is incorrect ("60.5" instead of 58). The student correctly states that the mean could be used to support the conclusion and clearly presents justification to show that the data does not provide support strong enough to make the conclusion valid ("even if he used the means the difference between them is less than two years"). This response demonstrates a conceptual understanding and analysis of the problem.

Score for Sample Student Response #14: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. All four measures of central tendency are correct. The student clearly indicates that in order for Sam to support his conclusion he should use the means. ("Sam could use the data to support his conclusion by using the mean of both Presidents' inaugurations, since the first term was 58.1, and the 2nd term was 56.8.") Logically sound and fully developed justification is presented to show that the data does not offer support strong enough to make Sam's conclusion valid. ("He's trying to say that the ages decreased, so he couldn't use the median, because that increases. I don't think it is a strong point to use though, because it only decreases by about 1.3 years. So it shows that it decreased, but not by much, so it might not be valid enough.") This response demonstrates a complete understanding and analysis of the problem.

Score for Sample Student Response #15: Rubric Score 1

Annotation: This response indicates little attempt to apply a reasonable strategy. All four measures of central tendency are correct; however, the student's comparison of the minimum and maximum ages of the two groups does not support the conclusion. The response incorrectly states that the data provides support strong enough to make the conclusion valid. Comparing the age ranges of the two sets of data cannot justify that the data is strong enough to make the conclusion valid. This response demonstrates a minimal understanding of the problem.

Score for Sample Student Response #16: Rubric Score 3

Annotation: This response indicates application of a reasonable strategy that leads to a correct solution in the context of the problem. Both the means and the medians are correct. The student correctly indicates that the means could be used to support the conclusion ("he should use the mean of the ages because median shows increase"). The student correctly states that the data does not provide strong enough support to make the conclusion valid. Justification that supports the solution and is logically sound also is given. "It needs more back up than just the means of the ages," and, therefore, the data would not be strong enough to make the conclusion valid. This response demonstrates a complete understanding and analysis of the problem.

Score for Sample Student Response #17: Rubric Score 2

Annotation: This response indicates an incomplete application of a reasonable strategy. All four measures of central tendency are correct. The response correctly identifies the mean as supporting the conclusion ("he could use the mean. It went from 58.1 to 56.8"). The student incorrectly states that the data is strong enough to make the conclusion valid. This response demonstrates a conceptual understanding and analysis of the problem.

Anchor Papers used in scoring