In descriptive statistics, which statement best describes what the mean represents for a set of numerical data?

• A. It always equals the most frequent value in the data set.
• B. It is unaffected by extremely large or small values (outliers).
• C. It is the value that splits the ordered data into two equal halves.
• D. It represents the arithmetic average and is often used as a measure of the center of the data.

Answer: (D)

Verified step by step guidance

1. Understand that the mean is a measure of central tendency, which summarizes a set of numerical data by identifying a central point.
2. Recall that the mean is calculated by adding all the values in the data set together and then dividing by the number of values, which gives the arithmetic average.
3. Recognize that the mean is sensitive to all values in the data set, including extremely large or small values (outliers), so it can be influenced by them.
4. Distinguish the mean from other measures of central tendency: the mode (most frequent value) and the median (value that splits the data into two equal halves).
5. Conclude that the mean represents the arithmetic average and is commonly used to describe the center of the data distribution.