Describe the main measures of central tendency and dispersion. Why are

While a measure of dispersion helps determine how evenly distributed the observations are within a dataset, a measure of central tendency aids in pinpointing a dataset's location.
The “location” of a dataset indicates a value, about which, most of the observations in the dataset are concentrated. The measure of central tendency is a central value in the dataset, which is typically the mean (arithmetic, geometric, or harmonic), median or mode. All these values give an idea about a “typical” value in the dataset. 
On the other hand, a dataset's "spread" reveals how widely spaced out the observations are. The spread in relation to the location value or the measure of central tendency is typically measured by an absolute measure of dispersion.
The typical measures of dispersion are variance, standard deviation, mean deviation about mean or median, etc. The average spread of the observations around the central value can be calculated using all of these values.
There are, as is obvious, two completely different sets of measurements, one used to determine the measures of central tendency and the other used to determine the measures of dispersion. Thus, a measure of central tendency cannot tell a researcher about the spread of the scores in the distribution. 
Mean 
Mean is the most widely used measure of Central Tendency that is used in Statistical analyses. It is most appropriate with a population that does not have wide fluctuations in data value, i.e. Outliers. Presence of Outliers (extremities) distort Mean. 
Mean is valid only if the Population has Interval data or Ratio Data that can be subjected to further algebraic treatment. However, the population must contain only symmetrical Interval data or Ratio data, for mean to be used as appropriate measure. 
Median 
Median is the appropriate measure when we either know for sure that the population has extreme values (outliers) or the distribution is Skewed, or there is a probability that the population distribution may be skewed. 
Median is also appropriate when there are only a small number of data points in the population (i.e. population size is small). 
Median is appropriate also because it is not much sensitive to changes in data value, since it points out the "center of the data set". 
When population data is qualitative (e.g. Rankings) and not quantitative, Median is appropriate to use. 
Mode 
Mode is most appropriate for a Population having Categorical (Nominal) data (e.g. identifying the most popular product in a set having 100 types of product). 
For a population having Interval or Ratio data, if the data is spread too thinly with no two data values being the same, Mode will not be appropriate to use or we can have a non-existent Mode as well. 
Dispersion: 
Variance, standard deviation, and mean deviation are three measures of dispersion. All these measures tell how much the data vary from their average. The common thing between these three measures is that they show how much the data varies from their mean. For finding the values of variance, standard deviation and mean deviation, one has to find the difference of the sample point from their mean. 
This is the common step for calculating the values of variance, standard deviation and mean deviation. The common thing is the variability from the mean, which helps to find the spread of the data set from the mean. Moreover, it helps to find the outliers also. As much variability indicates the presence of outliers.