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Mean, median and mode are all valid measures of central tendency, but under different situations, some measures of tendency become more appropriate to use than others. The different situations are when the populations are not uniform, that is when you use them separately according to the one that is suitable for that particular instance (Park, 2015).
One can use mean/ median or mode in a population that is uniform. A normal population will consist of same people with the same goal to achieve. An example of such population is students. In class, the measures of central tendency will be used to grade students after the results and get their mean. Another characteristic of a population that we can use the measures of central tendency is where the population is non-uniform regarding age, height, weight, etc. In such a situation, if we need to get a value that will be applied to that population, we need to get a normal number that will take care of the smallest and the biggest. The measure of central tendency will be mean. The mean will be the average of the total number of that population (Cuevas, 2014).
The other characteristic of a population that you can use measures of central tendency will be the gender. Regarding a gender, you may find that a certain gender is dominant. The number of males may be higher than that of females. In this case, the mode is used to know the type of gender that is high in number. Mode gives the highest number of an element that is repeated most (Park, 2015).
Reference
Cuevas, A. (2014). A partial overview of the theory of statistics with functional data. Journal of Statistical Planning and Inference, 147, 1-23.
Park, H. M. (2015). Univariate analysis and normality test using SAS, Stata, and SPSS.