Test of Essential Academic Skills (TEAS) ATI Mathematics Practice Test

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Which of the following statements regarding the histograms is true?

  1. Group A is negatively skewed and has a mean that is less than the mean of Group B.

  2. Group A is positively skewed and has a mean that is more than the mean of Group B.

  3. Group B is negatively skewed and has a mean that is more than the mean of Group A.

  4. Group B is positively skewed and has a mean that is less than the mean of Group A.

The correct answer is: Group B is negatively skewed and has a mean that is more than the mean of Group A.

To determine the truth of the statement regarding the histograms, it is essential to understand the concepts of skewness and how it affects the relationship between the mean and the shape of data distributions. In the case of Group B being negatively skewed, this indicates that the tail on the left side of the histogram is longer or fatter than the right side, which often results in the mean being lower than the median. If Group B's mean is more than the mean of Group A, it is consistent with the behavior of negatively skewed distributions where the mean could still align above the median, especially if a significant amount of data is concentrated towards the higher end of the scale. Therefore, if Group B has a mean that is less than that of Group A, it aligns well with the nature of negatively skewed distributions, which tend to pull the mean downwards relative to the median. Consequently, the true statement regarding the relationship between the histograms of the two groups is that Group B is negatively skewed and has a mean that is more than that of Group A, providing a valid statement regarding the comparative mean of the two groups. This illustrates the connection between the skewness of a distribution and the positioning of the mean, reinforcing why the selected statement

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