Question

the purpose of this pretest is to assess your mastery of the standards covered in this module. you will be able to take this pretest only one time. i exhibit mastery at a level of 60% or higher, you will be permitted to proceed to the next module without further review of the content.
if, however, you score below 60%, you will need to proceed through the items in this module to prepare for the module exam.
question 7
which event always occurs when one or more outliers are removed from a dataset?
the standard deviation for the dataset will decrease.
the standard deviation for the dataset will increase.
the mean for the dataset will increase.
the mean for the dataset will decrease.

Explanation:

• Standard Deviation Concept: Standard deviation measures the spread of data from the mean. Outliers are extreme values that are far from the main cluster of data. When outliers (which are far from the mean) are removed, the data points are closer to the mean, so the spread (measured by standard deviation) decreases.
• Mean Analysis: The mean can either increase or decrease depending on whether the outlier is a high or low value. For example, if the outlier is a very large value, removing it will decrease the mean; if the outlier is a very small value, removing it will increase the mean. So the mean does not always increase or decrease.
• Elimination of Other Options: The standard deviation cannot increase as removing outliers (which increase spread) reduces spread. The mean’s change depends on the outlier’s direction (high/low), so it’s not always increasing or decreasing. Thus, only the statement about standard deviation decreasing is always true.

Answer:

A. The standard deviation for the dataset will decrease.