Use the image to answer the question.

Question

A distribution curve is plotted by joining the four points A, B, C, and D on a plane.

A team of students were comparing the mean and median of a dot plot and noticed that the dots made a graph. They labeled the mean, median, minimum, and maximum of the graph. Which point is most likely the mean of the skewed data?

(1 point)
Responses

D
upper D

B
upper B

C
upper C

A

Answer 1

Since the distribution is skewed, the mean is typically pulled in the direction of the skew. If the data is skewed to the right (positively skewed), the mean will be greater than the median, often falling closer to the tail on the right. Conversely, if the data is skewed to the left (negatively skewed), the mean will be less than the median.

Without seeing the actual points and their positions on the graph, I can provide a general guideline based on the typical behavior of skewed distributions:

• If the distribution is skewed to the right, the mean will be to the right of the median.
• If the distribution is skewed to the left, the mean will be to the left of the median.

Usually, the mean is found at the tail end of the skew.

If you know the relative positions of points A, B, C, and D in relation to each other, select the point that is most distant from the median towards the direction of the tail of the distribution.

Please provide a description of the graph's skewness or the position of the points, and I’d be happy to help further! Otherwise, choose the point that is located towards the tail compared to the median, as that will likely represent the mean for skewed data.