10. A data set has a mean of 14.5 and a median of 11.2. Which of the following terms would describe this data set?
Answer: C
The data set is skewed right.
Given that the mean (14.5) is greater than the median (11.2), this indicates that the data set has a longer tail on the right side, which is characteristic of a right-skewed distribution.
A) Bimodal
A bimodal distribution has two modes, or peaks, in its frequency distribution. Since the question provides only the mean and median without any information about the frequency of values, there is no evidence to suggest that the data set has two distinct peaks, making this option incorrect.
B) Skewed left
A left-skewed distribution would have a mean that is less than the median, indicating that the tail on the left side is longer. In this case, since the mean is greater than the median, this option is not applicable to the data set.
C) Skewed right
This is the correct option. When the mean is greater than the median, it suggests that there are higher values pulling the mean upwards, which is typical of a right-skewed distribution. This means that the bulk of the data is concentrated on the left side, with a few higher values extending the tail on the right.
D) Symmetrical
A symmetrical distribution would have the mean and median equal, indicating that the data is evenly distributed around the center. Since the mean and median in this data set are different, it cannot be classified as symmetrical.
Conclusion
The data set is definitively classified as skewed right due to the mean being higher than the median, which indicates a longer tail on the right. Options A, B, and D fail to accurately describe the distribution's characteristics, reinforcing that C is the only correct choice.