At a certain restaurant, the distribution of wait times for customers is recorded and entered into a graphing calculator. Which of the following statistics would best describe the center of this distribution if the data are skewed to the right?

• A. The $\mathrm{mean}$
• B. The $\mathrm{median}$
• C. The $\mathrm{mode}$
• D. The $\mathrm{range}$

Answer: (B)

Verified step by step guidance

1. Understand the shape of the distribution: Since the data are skewed to the right, this means there is a longer tail on the right side of the distribution, indicating some larger values that pull the data in that direction.
2. Recall the properties of measures of central tendency: The mean is sensitive to extreme values (outliers) and can be pulled in the direction of the skew, while the median is more resistant to outliers and better represents the 'middle' of the data in skewed distributions.
3. Consider the mode: The mode represents the most frequent value but does not necessarily reflect the center of the data, especially in skewed distributions.
4. Evaluate the range: The range measures the spread between the smallest and largest values but does not describe the center of the distribution.
5. Conclude that the median is the best measure to describe the center of a right-skewed distribution because it is not affected by extreme values and better represents the typical wait time.