The importance of the mode, mean and median in business depends on the analysis required and the business function to which the results apply. For some data, the three values are close or the same, while for other types of data, the mode or median may differ substantially from the mean. When the three calculations give different results, the key is to choose the value that will give the desired guidance. This choice is different for different business functions.
General

The mode of a set of values is the value that occurs most frequently. The mean is the average, calculated by adding all the values and dividing by the number of values. The median is the value that is in the middle of the list of values when the values are listed in order of size. For a normal distribution, where most values are in a central range with a few at the high and low extremes, the mode, mean and median calculations give similar results. When there are large values at one extreme, or when a particular value occurs much more often than all others, the three calculations give different results. Their importance depends on the application of the data analysis.
Mode

The mode is the most important when an analysis is looking for what happens most often. In analyzing prices, most of the sales occur at a particular list price or possibly at a reduced, sale price. While there may have been sales at other prices, very few customers will have paid an average or a mean price. Those values are therefore less important when setting pricing in terms of what most customers paid.
Mean

The mean is the most important value when data is scattered, without a typical pattern. The mode may identify several values that occur frequently, and the median may be skewed if there are a lot of low values, but the mean catches all the values. Such patterns can occur in procurement, where costs vary according to external factors. The mean gives the average cost and forms a good basis for estimating future costs, as long as the external factors remain the same.
Median

The median is the most important value when the data has several values that occur frequently, and several comparatively very high values. The mode will not give a unique answer, and the mean will be skewed toward the higher values. An analysis of salaries often focuses on the amounts commonly paid but ignores extremes that are probably special cases. The median salary gives a value close to the average salary commonly paid, without taking the extreme values into consideration.
References
 Nova Southeastern University, Fischler School of Education and Human Services: Measures of Central Tendency: The Mean, Median and Mode
 Stanford University: Statistics Fundamentals, Measures of Central Tendency  Mean, Median and Mode
 Missouri State University; Introductory Statistics: Concepts, Models, and Applications; David W. Stockburger