What does the symbol x ̅ represent in statistics?

The symbol x̅ (pronounced "x bar") represents the mean in statistics. The mean is calculated by summing all the values in a dataset and then dividing by the number of values. This gives a measure of central tendency, providing an average that summarizes the entire dataset into a single value.

The mean is particularly useful because it takes into account every value in the dataset, making it sensitive to variations. This means if you have a data set where most values are close together, but there's one extreme outlier, the mean will shift towards that outlier, reflecting its influence.

In contrast, the median represents the middle value of a dataset when organized in ascending or descending order, while the mode is the value that appears most frequently. The range measures the spread between the maximum and minimum values in a dataset. Therefore, x̅ specifically and exclusively denotes the mean, distinguishing it from these other statistical measures.