a set of data has a high - value outlier. how do you expect the standard deviation to change when the…

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.

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.

Answer

Brief Explanations:

The standard deviation measures the spread of data. An outlier, whether high - value or low - value, increases the spread. When a high - value outlier is removed, the data becomes more clustered around the mean, reducing the spread and thus decreasing the standard deviation. Similarly, for a low - value outlier, its removal also makes the data more clustered around the mean, leading to a decrease in the standard deviation.

Answer:

When a high - value outlier is removed, the standard deviation is expected to decrease. When a low - value outlier is removed, the standard deviation is also expected to decrease. The result is the same in both cases because in either situation, the removal of the outlier makes the data more clustered around the mean, reducing the overall spread of the data.