Changing an x-value in a list affects the mean because the mean is the average of all values, while the variation, which measures the spread of those values, remains unaffected if all values are shifted equally. When only one value is altered, both the mean and the variance change due to the new distribution of values. The formula for the mean is the sum of all values divided by the number of values, while variance is calculated based on the squared differences from the mean. This distinction explains why the mean is sensitive to changes in individual values, whereas variation reflects the overall distribution. Understanding these mathematical principles clarifies the relationship between mean and variation in statistics.
