I agree with you that means is the average of components. Mean represents the sum of all components in a given dataset divided by the total number of the values (Black, 2009). I concur with you that the median is the middle number of a given set of data. For instance, if there are seven numbers in a given set of data, the median will be the number that falls between the third and fifth number. Moreover, if there are eight numbers in a certain set of data, then the median is obtained by calculating the average of the fourth and fifth numbers. A mode is the most common number in a given data set (Black, 2009). Mean is the most popular measure of central tendency. It is mostly used in continuous data. Also, mean is the measures of central tendency that produce the lowest amount of error in a given data set. Median is preferred over mean when data contains outliers because mean would be dominated by the outliers rather than the typical values. For example, the median is used to obtain the average income of a given country or city because it represents the middle group. The mode can be preferred over the median when calibrating an instrument to a specific temperature.
References
Black, K. (2009). Business Statistics: Contemporary decision making. John Wiley & Sons.