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

• A. It is always the most frequently occurring value in the $\mathrm{data}$.
• B. It represents the arithmetic center or $\mathrm{average}$ of the $\mathrm{data}$.
• C. It is the difference between the $\mathrm{largest}$ and $\mathrm{smallest}$ values.
• D. It is always the middle value when the $\mathrm{data}$ 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. The formula for the mean \( \bar{x} \) of a data set with values \( x_1, x_2, \ldots, x_n \) is given by: \[ \bar{x} = \frac{1}{n} \sum_{i=1}^n x_i \]
4. Note that the mean is not necessarily the most frequently occurring value (which is the mode), nor is it the middle value when data are ordered (which is the median), nor is it the range (difference between largest and smallest values).
5. Therefore, the best description of the mean is that it represents the arithmetic center or average of the data.