In the formula for the sample mean, X-bar equals which of the following?

• A. The sum of all data values
• B. The sum of all data values divided by n
• C. The product of all data values
• D. The square root of the sum of data values

Answer: (B)

The main idea is that the sample mean is the average value of the data set. It measures the center by treating every observation equally, so you add up all the values and then divide by how many observations there are. This dividing by the count is what converts the total into an average.

If you only looked at the sum, you’d have the total, not the central value. If you multiplied the data values, you’d get a product that tells you something entirely different, and taking the square root of the sum doesn’t yield an average either. For example, with values 3, 7, and 5, the sum is 15 and there are 3 observations, so the mean is 15 divided by 3, which equals 5.

So the expression for the sample mean is the sum of all data values divided by the number of data values.