if a score is change, will the mean be affected?
if a score is added in the data set, will the median be changed?
changing a score will change the mean
adding a score will change the median
... unless the score is equal to the median
The more a score is changed, the greater the effect on the mean, especially with small samples.
Assuming the score is not at the median, the median will change slightly. The change might be greater for small samples.
To answer your first question, whether a change in score affects the mean or not depends on the nature of the change. If a score is changed within the dataset, the mean will be affected. The mean is calculated by summing up all the scores and dividing by the total number of scores. So if a score is increased or decreased, it will impact the sum and thus alter the mean.
To answer your second question, if a new score is added to a dataset, it may or may not change the median. The median is the middle value in a dataset when the data is arranged in ascending or descending order. So, if the new score is close to the existing values and falls within the middle range, the median may not change. However, if the new score is larger or smaller than the existing values at the ends of the dataset, it will shift the middle position and change the median.
In both cases, it's important to note that the mean and median are statistical measures that provide different insights into a dataset. While the mean is sensitive to all values, the median is more robust and less influenced by extreme values.