Given a sample with a sample mean of $\overline{x}$ and a sample standard deviation of $s$, which of the following best describes the sample mean?

• A. It is the arithmetic average of all sample values.
• B. It is the value that occurs most frequently in the sample.
• C. It is the square root of the sum of squared deviations from the mean.
• D. It is the middle value when the sample data are arranged in order.

Answer: (A)

Verified step by step guidance

1. Understand the definition of the sample mean, often denoted as \(\overline{x}\), which is a measure of central tendency representing the average value of the sample data.
2. Recall the formula for the sample mean: \(\overline{x} = \frac{1}{n} \sum_{i=1}^{n} x_i\), where \(n\) is the sample size and \(x_i\) are the individual sample values.
3. Recognize that the sample mean is calculated by adding all the sample values together and then dividing by the number of observations, which makes it the arithmetic average.
4. Differentiate the sample mean from other statistics: the mode is the most frequently occurring value, the standard deviation involves the square root of squared deviations, and the median is the middle value when data are ordered.
5. Conclude that the sample mean is best described as the arithmetic average of all sample values.