Final answer:
The mean should be used when the data is symmetric or has extreme values, while the median or mode may be better choices when the data is skewed left or right.
Step-by-step explanation:
The mean should be used in cases where the data is symmetric or has extreme values. When the data has extreme values, the mean can provide a better representation of the overall average. Additionally, in symmetric distributions, the mean and median are close or the same, making the mean a suitable measure of central tendency.
For example, if we have a set of exam scores where most students score around the same mark, the mean would accurately represent the average performance.
On the other hand, when the data is skewed left or skewed right, the mean may not be the best choice. Skewed distributions have different spreads on each side, and the mean can be influenced by extreme values, making it less representative of the central tendency. Instead, the median or mode may be more appropriate measures of central tendency in these cases.
For instance, if we have a dataset of annual salaries where a few individuals earn extremely high incomes, the mean salary would be greatly influenced by these outliers and may not accurately represent the typical salary. Using the median or mode would provide a more representative measure of central tendency in this situation.