Averages

 

Averages are a bad idea. Averages hide characteristics, individual properties and specialities behind one value. Nobody wants to be average, in fact people tend to feel bad if their individual properties are not considered (no vegetarian meal in a restaurant). On the other side spotting individual strength and adressing them is a reliable approach to increase response e.g in a marketing campaign. Why would anyone even consider to write about average?

Because averages are useful!

Averages CAN hide characteristics and individual properties behind one value. In the right places they can contribute to massive simplifications, effective classifications and help to compare results. Averages help on regression and prediction and in the construction of clusters and decision trees, the most widely used data mining methods. They can be used for smaller subsets and applied in bigger scales. Therefore they are essential in data science.

From a mathematical point of view there are a lot of different ways to define averages, the most common average ("the average of the averages") is the arithmetic average, which sums up all of the values deviding them into the number of values (we only focus here on average used in practise, infinite rows are a nice, but a different field!). Another average is the geometric average of n numbers, in which all the n values are multiplied and the nth root is taken. And the harmonic average which however is not used that often.

In statistics the weighted average (or weighted mean) is of bigger importance, in it the different values are given a certain weight (usually the sum of all weights is 1). It does not treat all the values in the same way, some values are more important (higher weight) than others.

What does this have to do with the small town Haßloch in the Bad Dürkheim district in Germany?
Haßloch is an average. The distribution of the inhabitants considering age, income, education and domestic home size is representative for Germany, in other words the average on these values in whole Germany are pretty close to the values in Haßloch. Therefore Haßloch is the ideal place to test and analyze new product launches. Products that fail in Haßloch will not get released into the German market and lots of the successful products and packagings have made their way through the supermarkets of Haßloch.

By the way, the average German prefers the color blue, the average German man is a 1,78m tall, 82,4kg weighty blond or dark blond. You want to know, if you can recognize the average German girl (and other nations)? Find out here.