Which statement best describes the mean of a data set?

Which statement best describes the mean of a data set?

• A. The average of all values.
• B. The middle value when data are ordered.
• C. The most frequent value.
• D. The spread of the data (range).

Answer: (A)

The mean is the average of all values in a data set, found by adding every value together and dividing by how many values there are. This uses every data point to determine a single central value, which is exactly what “average” means in this context. For example, with values 2, 4, and 6, the mean is (2 + 4 + 6) / 3 = 4. This is the representative value that summarizes the data when no extreme outliers pull the set in a different direction. The other ideas describe different concepts. The middle value when data are ordered is the median. The most frequent value is the mode. The spread of the data (range) tells how wide the data are, not the central value. The mean works best as a measure of center when the data are fairly symmetric and without extreme outliers, which is why “the average of all values” correctly describes it.

The mean is the average of all values in a data set, found by adding every value together and dividing by how many values there are. This uses every data point to determine a single central value, which is exactly what “average” means in this context. For example, with values 2, 4, and 6, the mean is (2 + 4 + 6) / 3 = 4. This is the representative value that summarizes the data when no extreme outliers pull the set in a different direction.

The other ideas describe different concepts. The middle value when data are ordered is the median. The most frequent value is the mode. The spread of the data (range) tells how wide the data are, not the central value. The mean works best as a measure of center when the data are fairly symmetric and without extreme outliers, which is why “the average of all values” correctly describes it.