Which of the following is not an appropriate definition of the mean?

• A. A measure of central tendency calculated as $\frac{\sum x_i}{n}$
• B. The arithmetic average of a set of numbers
• C. The value that occurs most frequently in a data set
• D. The sum of all values in a data set divided by the number of values

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the concept of the mean. The mean is a measure of central tendency that represents the average value of a data set.
2. Step 2: Recognize the formula for the mean, which is given by \(\text{Mean} = \frac{\sum\limits_{i=1}^n x_i}{n}\), where \(x_i\) are the data points and \(n\) is the number of data points.
3. Step 3: Identify that the mean is also commonly described as the arithmetic average of a set of numbers, which aligns with the formula above.
4. Step 4: Note that the sum of all values divided by the number of values is another way to describe the mean, consistent with the formula.
5. Step 5: Understand that the value that occurs most frequently in a data set is called the mode, not the mean, so this is not an appropriate definition of the mean.