Which measure of central tendency is defined as the sum of all observations divided by the number of observations?

The mean is defined as the total of all observations divided by the number of observations. It provides a comprehensive measure of central tendency, as it takes into account every value in the dataset, allowing for an average that represents the entire group. This approach makes the mean particularly useful in many statistical analyses, as it conveys the overall level of the variable being measured.

For example, if you have a dataset of test scores from a class, calculating the mean gives you the average score, which helps understand the overall performance of the class. The mean can be significantly influenced by extreme values or outliers, which is a crucial point to consider when interpreting the data.

The other measures of central tendency do not operate in the same way. The median looks at the middle value of a dataset when it is ordered but does not incorporate all data points directly in its calculation. The mode identifies the most frequently occurring value in the dataset, which does not reflect the overall distribution of all data points. Lastly, the range measures the difference between the highest and lowest values in the dataset, thus failing to represent the central tendency of the group.