What is the formula used to calculate the mean of a set of observations?

The formula used to calculate the mean of a set of observations is indeed the sum of all observations divided by the number of observations. This method provides a representative average of the data set, taking into account all individual values. By adding up all the observations, you get the total, and dividing that total by the count of the observations gives you the mean, which essentially reflects the central tendency of the data. This calculation is foundational in statistics, as it provides a baseline for further analyses such as variance or standard deviation.

In contrast, other choices outline different statistical measures. The option describing the highest number minus the lowest number refers to the range, which indicates the spread of the data but does not provide an average. The option that identifies the most frequently observed number describes the mode, which tells us about the most common observation but does not consider the other values within the dataset. Lastly, the center number when arranged in order is the median, a different measure of central tendency that can be particularly useful in skewed distributions. Collectively, while these alternatives serve important purposes, they do not define the mean, which focuses on average value through a comprehensive approach.