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

• A. It is always equal to the $\mathrm{median}$.
• B. It represents the $\text{arithmetic center}$ of the data.
• C. It is the difference between the $\text{largest}$ and $\text{smallest}$ values.
• D. It is the most frequently occurring value in the data ($\mathrm{mode}$).

Answer: (B)

Verified step by step guidance

1. Understand the definition of the mean: The mean is the arithmetic average of a data set, calculated by summing all the values and dividing by the number of values.
2. Recall the formula for the mean: \(\text{Mean} = \frac{\sum_{i=1}^n x_i}{n}\), where \(x_i\) represents each data value and \(n\) is the total number of values.
3. Compare the mean to other measures of central tendency: The median is the middle value when data is ordered, and the mode is the most frequently occurring value.
4. Recognize that the mean is not necessarily equal to the median or mode, and it is not a measure of spread like the range (difference between largest and smallest values).
5. Conclude that the mean best describes the arithmetic center of the data, representing the balance point of the data distribution.