Given the test scores of 7, 11, 5, 6, and 11, which measure of central tendency would change the most if a score of 2 was added?

Given the test scores of 7, 11, 5, 6, and 11, which measure of central tendency would change the most if a score of 2 was added?

• A. Mean
• B. Median
• C. Mode
• D. Range

Answer: (D)

When evaluating how the addition of a score affects measures of central tendency, the focus here is on which measure will demonstrate the most significant change. The range, defined as the difference between the highest and lowest scores in a data set, will be notably affected by the addition of the score of 2. Initially, the highest score in the original data set (7, 11, 5, 6, 11) is 11, and the lowest is 5. This results in a range of 11 - 5 = 6. However, with the addition of the score of 2, the lowest score in the set becomes 2. Now the range will be recalculated as 11 - 2 = 9, demonstrating an increase of 3. In contrast, the mean (average) will also change, but not as dramatically since it is calculated based on all the values. The median, which is the middle number in an ordered list, is less sensitive to extreme values like the addition of a very low score. Since there are two modes (11 appears most frequently), the mode will remain unaffected by the introduction of the lower score. Therefore, among the options, the range exhibits the most noticeable shift

When evaluating how the addition of a score affects measures of central tendency, the focus here is on which measure will demonstrate the most significant change.

The range, defined as the difference between the highest and lowest scores in a data set, will be notably affected by the addition of the score of 2. Initially, the highest score in the original data set (7, 11, 5, 6, 11) is 11, and the lowest is 5. This results in a range of 11 - 5 = 6. However, with the addition of the score of 2, the lowest score in the set becomes 2. Now the range will be recalculated as 11 - 2 = 9, demonstrating an increase of 3.

In contrast, the mean (average) will also change, but not as dramatically since it is calculated based on all the values. The median, which is the middle number in an ordered list, is less sensitive to extreme values like the addition of a very low score. Since there are two modes (11 appears most frequently), the mode will remain unaffected by the introduction of the lower score.

Therefore, among the options, the range exhibits the most noticeable shift