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:

The standard deviation measures the spread of data. A high - value outlier increases the spread, so removing it will decrease the standard deviation. Similarly, a low - value outlier also increases the spread of the data set. Removing it will also decrease the standard deviation. In both cases, the outlier is a data point far from the mean, and its removal makes the data more clustered around the mean, reducing the overall spread.

Answer:

When a high - value outlier is removed, the standard deviation is expected to decrease. If there was a low - value outlier instead and it was removed, the standard deviation would also decrease.