Last updated on 4/28/21

## Understand the Purpose of Univariate Analysis What do the following have in common: the average age of the population of China in 2010, the pass rate for the quiz at the end of Part 1 of this course, and the soil erosion index for the Hauts de France region in France?

Formally, a statistic is a numerical indicator calculated on the basis of a sample. The average age is calculated on the basis of the residents of the country, the pass rate of a quiz is calculated on the basis of student responses, and the soil erosion index is calculated on the basis of samples taken from plots of land.

In other words, as soon as you calculate a number based on a sample, you’re generating statistics!

Statistics are useful, because they enable us to reduce characteristics of a large sample to a single number! Of course, a lot of information gets lost in the calculation; for example, you can calculate a pass rate based on student responses, but you can’t find student responses from a pass rate alone!

So, a statistic is an indicator (of lesser or greater utility) of a specific characteristic of a sample.

You might also run across the term statistical index. A statistical index is a statistical measure developed according to a certain vision, based on specialized knowledge in a specific field (the economy, for example). You could say that an index is a statistic embedded in a philosophy. Unlike an index, an indicator (such as an average, for example) is entirely neutral.

The reason we develop so many indices and indicators is that, when we’re trying to make decisions, they can point us in the right direction (as their name suggests!). For example, economic, environmental, and sociological indicators are used to help make political decisions.

Some indicators and indices are developed on the basis of very simple calculations, such as a company’s sales figures (which are obtained simply by adding up all of the company’s receipts).

However, others require more complex calculations, such as those involving more than one characteristic of a population. This is the case for the Human Development Index (HDI), which is developed on the basis of per capita GDP, life expectancy at birth, and education level. There is also a relational capacity indicator, which measures the quality of relationships between people and their level of relational autonomy.

In the environmental field, we find indices of "biocapacity" and “human environmental footprint,” which are calculated on the basis of data concerning forests, developed land, agricultural fields, etc.

Of course, many different indicators can be developed for a single population. Each of them tells us something about a specific characteristic of that population. For example, the class average on an exam tells us whether the exam had a good pass rate. But the standard deviation (more on this soon) of the grades of this same population tells us whether there were major discrepancies between students.  