In statistics, what is the mean of a data set with values $x1$, $x2$, ..., $xn$?

• A. The largest value minus the smallest value in the data set
• B. The middle value when the data are ordered (or the average of the two middle values if $n$ is even)
• C. The sum of the values divided by the number of values: $\frac{{\sum }_{i=1}^{n}xi}{n}$
• D. The value that occurs most frequently in the data set

Answer: (C)

Verified step by step guidance

1. Understand that the mean of a data set is a measure of central tendency that represents the average value of all data points.
2. Identify the data set values as \( x_1, x_2, \ldots, x_n \), where \( n \) is the total number of values.
3. Calculate the sum of all the data values using the summation notation: \( \sum_{i=1}^{n} x_i \). This means adding each value from \( x_1 \) to \( x_n \).
4. Divide the total sum by the number of values \( n \) to find the mean. This is expressed as: \[ \text{Mean} = \frac{\sum_{i=1}^{n} x_i}{n} \]
5. Interpret the result as the average value of the data set, which balances all the values around this central point.