Measures of Center
Best Measure
Different measures of center are appropriate for different data sets. When choosing the best measure for the data, always try to find all three to have as much information as possible. Mode is the only possible measure when dealing with categorical variables and should also be chosen when asked for the most popular response. Mean is the measure of center that is affected by outliers. A large outlier will skew the mean high and a small outlier will skew the mean low. When an outlier is present, the median is the best measure of center to represent the data. Mean is the best measure of center when there is no outlier.
Example 1
Which is the best measure of center for real estate values in a county where there is both inland and lake front property?
Since the price of lake front property is considerably higher than inland property, it would represent an outlier. Median is the best representation of this data.
Example 2
Which is the best measure of center for a company where 100 employees earn $5000 per year and the CEO makes $2,000,000 per year?
The CEO would be considered an outlier and skew the mean high. When representing the employees, the mode would be the best choice.