Which of the following best describes the $\mathrm{mean}$ in a data set?

• A. It is the difference between the largest and smallest values.
• B. It represents the arithmetic center or $\text{average}$ of the data.
• C. It is always the most frequently occurring value in the data.
• D. It is always the middle value when the data are ordered.

Answer: (B)

Verified step by step guidance

1. Understand that the mean is a measure of central tendency, which summarizes a data set with a single value representing its center.
2. Recall the definition of the mean: it is the arithmetic average of all the values in the data set.
3. Recognize that the mean is calculated by adding all the data values together and then dividing by the number of values, expressed as \(\text{Mean} = \frac{\sum x_i}{n}\), where \(x_i\) are the data points and \(n\) is the total number of points.
4. Differentiate the mean from other measures: the range (difference between largest and smallest), the mode (most frequently occurring value), and the median (middle value when data are ordered).
5. Conclude that the mean best describes the arithmetic center or average of the data, which is why the correct description is that it represents the arithmetic center or average.