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

• A. It is the value that divides the data set into two equal halves.
• B. It represents the $\mathrm{arithmetic center}$ of the data by averaging all values.
• C. It is always the most frequently occurring value in the data set.
• D. It is the difference between the largest and smallest values in the data set.

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 the center.
2. Recall that the mean is calculated by adding all the values in the data set together and then dividing by the number of values.
3. Recognize that the mean is also called the arithmetic average, and it balances the data values around it.
4. Differentiate the mean from other measures: the median divides the data into two equal halves, the mode is the most frequently occurring value, and the range is the difference between the largest and smallest values.
5. Conclude that the mean best describes the arithmetic center of the data by averaging all values.