Use the image to answer the 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

A
upper A

C
upper C

B
upper B
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1 answer

To determine which point likely represents the mean of a skewed data distribution, it's important to remember that the mean is sensitive to extreme values and is pulled in the direction of the skew. In a right-skewed distribution, the mean is greater than the median and will typically lie to the right of the median. Conversely, in a left-skewed distribution, the mean is less than the median and is located to the left.

If the points A, B, C, and D represent the mean, median, minimum, and maximum, and assuming the distribution is skewed to the right, we can conclude that the mean would be positioned to the right of the median. If the distribution is skewed to the left, the mean would be to the left of the median.

Based on this information, without seeing the actual placement of the points A, B, C, and D, I would suggest examining where the median is located in relation to the other points.

If we assume a right-skewed distribution and point B is the median, then the mean (which is pulled to the right) would most likely be D.

Conversely, in a left-skewed distribution, if B is the median, then the mean would likely be A.

Please analyze the positions of these points relative to each other on the curve to find the correct answer based on the skew direction.