64. Which distribution would have a mean and median that are approximately equal after an analysis of each employee’s number of customer service calls over the last month?
Answer: D
Normal distribution
A normal distribution exhibits symmetry around its mean, resulting in the mean and median being approximately equal. This characteristic makes it the ideal choice in scenarios where data is evenly distributed around a central value.
A) Pareto distribution
A Pareto distribution is typically skewed, with a long tail on one side. This skewness causes the mean to be greater than the median, thus making it unsuitable for situations where the mean and median need to be approximately equal.
B) Multimodal distribution
A multimodal distribution has multiple peaks, which can lead to a mean that is not representative of the central tendency of the data. The presence of multiple modes can create disparities between the mean and median, making this option incorrect.
C) Bimodal distribution
Similar to multimodal distributions, a bimodal distribution has two distinct peaks. This characteristic can lead to significant differences between the mean and median, especially if the two modes are far apart, thus failing to satisfy the condition of approximate equality.
D) Normal distribution
A normal distribution is characterized by its bell-shaped curve, where the data points are symmetrically distributed around the mean. This perfect symmetry ensures that the mean and median are equal, making it the correct choice for this question.
Conclusion
The normal distribution is the only option where the mean and median are approximately equal due to its symmetrical nature. In contrast, the other distributions—Pareto, multimodal, and bimodal—are characterized by skewness or multiple peaks, which disrupt the balance between mean and median. Therefore, the normal distribution is definitively the correct answer in this context.