Which of the following best describes the mean of a data set?

• A. It is the middle value when the data points are arranged in order.
• B. It is the difference between the largest and smallest values in the data set.
• C. It is the most frequently occurring value in the data set.
• D. It is the sum of all data points divided by the number of data points, $\mathrm{mean}=\frac{\sum x_i}{n}$.

Answer: (D)

Verified step by step guidance

1. Understand that the mean of a data set is a measure of central tendency, which summarizes the data with a single value representing the center of the data distribution.
2. Recall the definitions of other common measures of central tendency and spread: the median is the middle value when data are ordered, the range is the difference between the largest and smallest values, and the mode is the most frequently occurring value.
3. Identify that the mean is calculated by adding all the data points together to get the total sum of the values.
4. Divide this total sum by the number of data points in the set to find the average value.
5. Express the mean mathematically as: \(\text{Mean} = \frac{\sum_{i=1}^n x_i}{n}\), where \(x_i\) represents each data point and \(n\) is the total number of data points.