In statistics, what does the $\mathrm{mean}$ represent in a set of numbers?

• A. The $\mathrm{mean}$ is the difference between the largest and smallest values in the set.
• B. The $\mathrm{mean}$ is the average value, calculated by adding all the numbers together and dividing by the total count: $\mathrm{mean}=\frac{\sum x}{n}$.
• C. The $\mathrm{mean}$ is the middle value when the numbers are arranged in order.
• D. The $\mathrm{mean}$ is the most frequently occurring value in the set.

Answer: (B)

Verified step by step guidance

1. Step 1: Understand that the mean is a measure of central tendency, which summarizes a set of numbers by identifying a central point.
2. Step 2: Recognize that the mean is calculated by adding all the values in the data set together. This sum represents the total combined value of all observations.
3. Step 3: Count the total number of values in the data set. This count is important because the mean is an average, so it depends on how many values are included.
4. Step 4: Divide the sum of all values by the total number of values. This division gives the average value, which is the mean.
5. Step 5: Interpret the mean as the balance point of the data set, where the values are evenly distributed around this average.