Question

determine whether the following statement is true or false. if it is false, rewrite it as a true statement.

the mean is the measure of central tendency most likely to be affected by an outlier.

choose the correct answer below.

a. the statement is false. the median is the measure of central tendency most likely to be affected by an outlier.
b. the statement is true.
c. the statement is false. outliers do not affect any measure of central tendency.
d. the statement is false. the mode is the measure of central tendency most likely to be affected by an outlier.

Explanation:

Analyze the given statement

The statement is: "The mean is the measure of central tendency most likely to be affected by an outlier."

Evaluate the effect of outliers on measures of central tendency

• The mean is calculated by summing all values and dividing by the total count, making it highly sensitive to extreme values (outliers).
• The median is the middle value of an ordered dataset, which is resistant to outliers.
• The mode is the most frequently occurring value, which is also generally unaffected by outliers.
• Therefore, the statement is true.

Match with the multiple-choice options

• Option A states the statement is false and names the median.
• Option B states the statement is true.
• Option C states the statement is false and claims outliers do not affect any measure.
• Option D states the statement is false and names the mode.
• Thus, Option B is the correct choice.

Answer:

• A. The statement is false. The median is the measure of central tendency most likely to be affected by an outlier.
• B. The statement is true. (Correct answer)
• C. The statement is false. Outliers do not affect any measure of central tendency.
• D. The statement is false. The mode is the measure of central tendency most likely to be affected by an outlier.