A researcher computed the mean, the median and the standard deviation for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?
When a constant value is added to each score in a data set, it has the following effects on statistical measures:
Mean (Average): Adding a constant to each score will also add the same constant to the mean. Therefore, the mean will change.
Median: Adding a constant to each score does not affect the relative ordering of the scores, so it does not change the position of the median within the ordered data set. Therefore, the median will not change.
Standard Deviation: Adding a constant to each score does not change the variability within the data set, which is what the standard deviation measures. Therefore, the standard deviation will not change.
So, when 5 is added to each score, the mean and the median will change, but the standard deviation will remain the same. The correct answer is "The mean and the median."
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