Question

question 21 points 2

which of the following sentences about outliers is true?

the outlier will usually greatly affect the mean.

the outlier will usually greatly affect the mode.

Explanation:

Analyze the impact of outliers on measures of center

Using the Outlier Effects knowledge point

• Outliers are extreme values that lie far away from the rest of the data points in a distribution.
• The mean is calculated by summing all values and dividing by the total count, making it highly sensitive to extreme values.
• The mode is simply the most frequently occurring value in a dataset, which is generally unaffected by a single extreme outlier.

Evaluate the given statements

Using the Outlier Effects knowledge point

• Statement 1: "The outlier will usually greatly affect the mean." This is true because the numerical value of the outlier directly pulls the sum (and thus the average) toward it.
• Statement 2: "The outlier will usually greatly affect the mode." This is false because an outlier is typically a unique extreme value and does not alter the frequency of the most common values.

Answer:

• The outlier will usually greatly affect the mean. (Correct answer)
• The outlier will usually greatly affect the mode.