Which of the following best describes the $\mathrm{mean}$ in a data set?

• A. It is always equal to the $\mathrm{median}$ in any data set.
• B. It is the most frequently occurring value in the data.
• C. It is the value that divides the data into four equal parts.
• D. It represents the arithmetic center or balance point of the data.

Answer: (D)

Verified step by step guidance

1. Understand the definition of the mean: The mean is the arithmetic average of a data set, calculated by summing all the values and dividing by the number of values.
2. Recall the formula for the mean: \(\text{Mean} = \frac{\sum_{i=1}^n x_i}{n}\), where \(x_i\) represents each data value and \(n\) is the total number of values.
3. Compare the mean to other measures of central tendency: The median is the middle value when data is ordered, the mode is the most frequently occurring value, and quartiles divide data into four equal parts.
4. Recognize that the mean represents the balance point of the data because it takes into account all values and their magnitudes, unlike the median or mode.
5. Conclude that the best description of the mean is that it represents the arithmetic center or balance point of the data.