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Walter’s history test scores and Janine’s history test scores are shown on the dot plots below.

Walter’s History Test Scores
A dot plot tilted Walter's History Test Scores. A number line going from 80 to 90. There are 0 dots above 80, 81, and 82, 1 above 83, 2 above 84, 2 above 85, 2 above 86, 2 above 87, 0 above 88 and 89, and 1 above 90.

Janine’s History Test Scores
A dot plot tilted Janine's History Test Scores. A number line going from 80 to 90. There are 0 dots above 80, 81, 82, and 83, 3 above 84, 2 above 85, 2 above 86, 3 above 87, and 0 above 88, 89, and 90.

If each student gets 65 on the next test, which explains the measure of center that would be most affected?
Their means will be most affected because this value will be an outlier.
Their modes will be most affected because the distribution has changed.
Janine’s median will be more affected than Walter’s median because her overall scores were greater.
Walter’s median will be more affected than Janine’s median because there was a gap in his data.

1 answer

To determine which measure of center would be most affected by each student scoring 65 on their next test, let's analyze the implications for each of the options given:

  1. Means: The mean is calculated by taking the average of all scores. Adding a score of 65 (which is significantly lower than the current scores) will decrease the means for both Walter and Janine. Since this score is an outlier relative to their existing scores, it will have a more pronounced effect on the mean.

  2. Modes: The mode represents the most frequently occurring score in a dataset. Since 65 is not currently in either student's scores, the mode will not be directly affected. In fact, neither of their sets has an outlier that would change the mode.

  3. Medians: The median is the middle value when scores are arranged in order. Adding a score of 65 will shift the distribution, but how much it affects the median depends on how many scores are present and where the new score falls in the ranking. Walter’s scores are more clustered at the higher end with a larger gap, so the new score could have a more significant effect on his median compared to Janine's scores, which are also higher but more uniform in distribution.

Final Analysis: The mean will be affected most significantly due to the addition of an outlier (65), resulting in a greater shift away from the existing average for both students. The median is likely to be affected, but the degree of effect varies, and the evidence does not strongly support one student's median being more affected than the other without further calculations.

Conclusion: Therefore, the best explanation is:

Their means will be most affected because this value will be an outlier.