Which of the following is true of the $\mathrm{mean}$ of a set of data?

• A. The $\mathrm{mean}$ is always equal to the $\mathrm{median}$.
• B. The $\mathrm{mean}$ is the most frequently occurring value in the data set.
• C. The $\mathrm{mean}$ is unaffected by extreme values in the data set.
• D. The $\mathrm{mean}$ is the $\frac{\sum x}{n}$ of all data values divided by the number of values.

Answer: (D)

Verified step by step guidance

1. Recall the definition of the mean (or average) of a data set: it is calculated by summing all the data values and then dividing by the total number of values.
2. Express this mathematically as: \(\text{Mean} = \frac{\sum_{i=1}^n x_i}{n}\), where \(x_i\) represents each data value and \(n\) is the number of values.
3. Understand that the mean is a measure of central tendency, but it is not necessarily equal to the median (the middle value when data is ordered) or the mode (the most frequently occurring value).
4. Recognize that the mean is sensitive to extreme values (outliers), meaning that very high or very low values can significantly affect the mean.
5. Therefore, the true statement about the mean is that it is the sum of all data values divided by the number of values.