Describe the mean, mode, and median and give an example of each on how you use it everyday that makes each meaningful in its own way.

Solution: Mean, mode and median correspond to descriptive central measures of a sample. The mean corresponds to the simple average of the data, given by:

The means represents the “average” behavior of a sample and it’s considered as a representative value of the sample. For example, we could get a random sample of people from a certain neighborhood and obtain people’s yearly income. If we compute the mean of that sample, we obtain the “average yearly income” of the people selected in the sample, and more or less it should represent the income level of the sampled neighborhood.

The median is another central measure statistics which “represents” the sample in a different way, finding the point where 50% of the cases are above that point and 50% of cases are below. Median and mean don’t necessarily coincide (they only coincide if the distribution is symmetric). In some circumstances the median is a more appropriate indicator than the mean. For instance, if we measure the level of income of the nation, in terms of determine the well being of the citizens, a high mean income doesn’t indicate much about the well being of the citizens, since a few could be making a huge amount of money, when the majority could be living under the poverty line. For that kind of situations, the median is a more appropriate measure.

The mode is another statistics which corresponds to the outcome which repeats the most in the sample. The problem with this indicator is that it could be undefined, like for instance, no outcome is repeated in the sample. When it is well defined, it represents the “most popular” outcome of the sample, and it could have a value in its own. For instance, a toy company could be interested in knowing the kid’s preference for their different toys for this Christmas. If they sample a certain number of kids, and they ask which toy they prefer for Xmas, they are more interested in the mode of the sample, rather than the mean.