Final answer:
In both positively or negatively skewed distributions, the median provides a better representation of the data's center than the mean, as it is not influenced by the extreme values that skew the data. The correct answer is b) A negatively skewed distribution.
Step-by-step explanation:
The question asks which type of distribution would require using the median instead of the mean. When considering symmetric distributions like a normal distribution, the mean and the median are both centrally located and are typically equal.
However, in the case of positively skewed or negatively skewed distributions, the mean is pulled in the direction of the tail, while the median tends to align closer to the mode, which is the highest point of the distribution.
For bimodal distributions, the measure of center that should be used can vary because the mean might not represent the data accurately if the two modes are far apart.
Therefore, either a positively skewed distribution (a) or a negatively skewed distribution (b) would be instances where using the median instead of the mean would provide a better representation of the data's center, as the median is less affected by the skew.