Question

investigating variability
the standard deviation would ______ if outliers were removed because the data in the distribution would display ______ variability.
the standard deviation would ______ if outliers were added because the data in the distribution would display ______ variability.
reasoning with standard deviation
the standard deviation is more appropriate to use with ________ data sets.
the standard deviation of class b is ________ than the standard deviation of class a.

Explanation:

Step1: Understand standard - deviation and outliers

Standard deviation measures data spread. Outliers are extreme values.

Step2: Effect of removing outliers

When outliers are removed, data is less spread - out. So standard deviation decreases and variability is lower.

Step3: Effect of adding outliers

When outliers are added, data becomes more spread - out. So standard deviation increases and variability is higher.

Step4: Appropriate data for standard deviation

Standard deviation is more appropriate for symmetric data sets as it is based on the mean and is affected by extreme values.

Step5: Compare standard deviations visually

Without specific values, if Class B data is more spread out visually than Class A, its standard deviation is larger.

Answer:

• The standard deviation would decrease if outliers were removed because the data in the distribution would display lower variability.
• The standard deviation would increase if outliers were added because the data in the distribution would display higher variability.
• The standard deviation is more appropriate to use with symmetric data sets.
• (Without specific data values for Class A and Class B, assume based on spread) If Class B data is more spread out, the standard deviation of Class B is larger than the standard deviation of Class A.