Question

select the correct answer.

which statement is true?

• the mean lies to the right of the median for a positively skewed distribution.
• the mean lies to the left of the median for a positively skewed distribution.
• the mean lies to the left of the median for a symmetric distribution.
• a distribution skewed to the right is said to be negatively skewed.
• a distribution skewed to the left is said to be positively skewed.

Explanation:

Analyze the relationship between mean and median in skewed distributions

For a positively skewed (skewed to the right) distribution, the long tail is on the right side. This pulls the mean toward the higher values, meaning the mean is greater than the median. Therefore, the mean lies to the right of the median.

Evaluate the given statements

• "The mean lies to the right of the median for a positively skewed distribution." (True)
• "The mean lies to the left of the median for a positively skewed distribution." (False)
• "The mean lies to the left of the median for a symmetric distribution." (False, they are approximately equal)
• "A distribution skewed to the right is said to be negatively skewed." (False, it is positively skewed)
• "A distribution skewed to the left is said to be positively skewed." (False, it is negatively skewed)

Answer:

• (A) The mean lies to the right of the median for a positively skewed distribution. (Correct answer)
• (B) The mean lies to the left of the median for a positively skewed distribution.
• (C) The mean lies to the left of the median for a symmetric distribution.
• (D) A distribution skewed to the right is said to be negatively skewed.
• (E) A distribution skewed to the left is said to be positively skewed.