Question

which of the following statements about the mean are correct?
a. the mean represents a typical data point in a set.
b. the mean is the sum of all of the data points.
c. the mean equals the sum of the data points divided by the number of data points.
d. the mean must be an actual data point in a set.

Explanation:

• Option a: The mean is a measure of central tendency that represents a typical or average value in a data set, so this is correct.
• Option b: The sum of all data points is the total, not the mean. The mean is the average, so this is incorrect.
• Option c: By definition, the mean (or average) is calculated as the sum of the data points divided by the number of data points, so this is correct.
• Option d: The mean does not have to be an actual data point. For example, in the data set {1, 2, 3}, the mean is 2 (which is a data point), but in {1, 2, 4}, the mean is $\frac{1 + 2 + 4}{3}=\frac{7}{3}\approx2.33$, which is not a data point. So this is incorrect.

Answer:

a. The mean represents a typical data point in a set, c. The mean equals the sum of the data points divided by the number of data points