Best Measure of Center

What is the best measure of center? There is no single best answer to this question.

The table below shows a comparison of mean, median, mode, and midrange.

Measure of center (Average)	Definition	Does it exist?	Takes every value into account?	Affected by extreme values	How often is it used?
Mean	$\frac{\sum x_{}^{} }{number\ of\ values}$	Always exists	yes	yes	Used a lot
Median	Number in the middle	Always exists	no	no	Commonly used
Mode	Most frequent number(s)	May not exist. May be more than one mode.	no	no	Sometimes used
Midrange	$\frac{high + low}{2}$	Always exists	no	yes	Rarely used

As you can see in the table above, these measures of center have some similarities and differences.

As a rule of thumb, the best measure of center may depend on the kind of data set you have.

When do I use the mean? If it is important to include all the values and there are no extremes values, then use the mean.Generally speaking, this is your first choice.

When do I use the median? If there are some extreme values and not many values that repeat themselves, then use the median.

When do I use the mode? If there are many values that repeat themselves, then use the mode.

When do I use the midrange? If there are absolutely no extreme values, no repeated values, and you want to get an a quick answer for the measure of center, use the midrange. This is your last resort!