What impact do outliers have on the mean?

Outliers significantly influence the mean, primarily by inflating its value. The mean is calculated by summing all values in a data set and dividing by the number of values. When there are extreme values, known as outliers, in the data set—particularly high numbers—they can pull the mean upward.

For example, consider a scenario where a data set includes values like 2, 3, 4, and 100. The presence of the outlier (100) raises the total sum and consequently drives the mean higher than it would be if you only considered the other numbers. This effect demonstrates the sensitivity of the mean to extremes, highlighting why the mean may not always be the best central tendency measure in the presence of outliers.

In comparison, other options do not correctly capture the relationship between outliers and the mean. For instance, stating that outliers have no impact underestimates their influence, and suggesting they always decrease the mean overlooks the cases where outliers are high values. The notion of moderate impact also does not accurately reflect how dramatically an outlier can skew the mean in particular situations. Overall, recognizing the capacity of outliers to significantly inflate the mean is crucial for accurate data analysis and decision-making.