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

• A. It represents the arithmetic center or $\frac{\sum x_i}{n}$ (average) of the data.
• B. It is always the most frequently occurring value in the data.
• C. It is the difference between the largest and smallest values ($\mathrm{range}=x_{\max }-x_{\min }$).
• D. It is the value that divides the data into two equal halves ($\mathrm{median}$).

Answer: (A)

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. Calculate the mean by adding all the data values together and then dividing by the number of values. Mathematically, this is expressed as: \(\text{Mean} = \frac{\sum_{i=1}^n x_i}{n}\), where \(x_i\) are the data points and \(n\) is the total number of data points.
4. Compare the mean to other measures mentioned: the mode (most frequently occurring value), the range (difference between largest and smallest), and the median (value dividing data into two equal halves).
5. Conclude that the mean best fits the description of the arithmetic center or average of the data.