I am going to speak a little bit about Statistics. The topic today are “averages”. Suppose you have a set of “measurements” where . Then you can define the following quantities:
Remark: In the harmonic mean we need that every measurement is not null, i.e.,
There are some other interesting “averages”/”means”:
Generalized p-th mean.
where are the weight functions and they satisfy
A particularly important case occurs when the weight equals to inverse of the so-called variance of a population with finite size (generally denoted by ), i.e., when , the weighted mean yields:
Finally, a “naive” and usually bad statistical measure for a sample or data set is the midrange. Really, it is a mere measure of central tendency and no much more:
Here, refer to the maximum and minimum value of the sampled variable x in the full data set .
Many of the above “averages” have their own relative importance in the theory of Statistics. But that will be the topic of a future blog post handling statistics and its applications.
What average do you like the most? Are you “on the average”? Are you “normal”? 😉 Of course, you can consult your students, friends or family if they prefer some particular mean/average over any other in their grades/cash sharing, or alike :). See you soon in other blog post!