Which of the following correctly explains how to find the mean of a data set with values $x_1,x_2,\dots ,x_n$?

• A. Find the value that occurs most frequently in the data set.
• B. Sort the data and choose the middle value (or average the two middle values if $n$ is even).
• C. Multiply all the values together and divide by the number of values: $\overline{x}=\frac{x_1\times x_2\times \dots \times x_n}{n}$.
• D. Add all the values and divide by the number of values: $\overline{x}=\frac{x_1+x_2+\dots +x_n}{n}$.

Answer: (D)

Verified step by step guidance

1. Identify the data set values as \(x_1, x_2, \ldots, x_n\), where \(n\) is the total number of values in the data set.
2. Understand that the mean (or average) is a measure of central tendency that summarizes the data by a single value representing the center of the data distribution.
3. To find the mean, first add all the values together: calculate the sum \(S = x_1 + x_2 + \cdots + x_n\).
4. Next, divide the sum \(S\) by the number of values \(n\) to find the mean: \(\overline{x} = \frac{S}{n} = \frac{x_1 + x_2 + \cdots + x_n}{n}\).
5. This formula gives the average value of the data set, which is different from other measures like the mode (most frequent value) or median (middle value when sorted).