Question

a set of data has a high - value outlier. how do you expect the standard deviation to change when the outlier is removed? would the result be different if the data had a low - value outlier instead? explain.

Explanation:

Standard deviation measures data spread from the mean. A high-value outlier increases the mean and the squared differences from the mean, raising the standard deviation. Removing it reduces spread, so standard deviation decreases. A low-value outlier also increases spread by pulling the mean down and creating large squared differences. Removing it also reduces spread, so standard deviation decreases. The direction of change is the same for both outlier types.

Answer:

When a high-value outlier is removed, the standard deviation will decrease. The result would NOT be different for a low-value outlier: removing it will also cause the standard deviation to decrease. Both high and low outliers increase the overall spread of the data, so removing either reduces the data's variability, which lowers the standard deviation.