Statistics - Topics

What are statistics and why are they important?

Although mathematics is not popular, it is useful in life. Maybe none of us use Pythagoras' theorem daily but often – perhaps even subconsciously – when making decisions on various subjects, we calculate the probabilities of events that are supposed to help us make a rational decision. You most likely have calculated the difference in prices when buying any products or offers. Mathematics is part of our lives whether we like it or not!

An interesting part of mathematics is statistics. Every day, on social media, we are showered with statistics even if we don't consciously pay attention to them anymore. "Such and such a percentage of Poles may contract coronavirus", "such and such a percentage of the population voted for this or that presidential candidate" – these are examples, among many, which are multiplying in our lives. But what do statistics mean, what are they?

Statistics are used to generalise. According to calculated trends, you can predict certain situations as well as check the popularity of certain companies on the market. Some people use statistics to decide, for example, whether to invest in particular financial instruments. Statistics are supposed to represent a general picture of society or to present general situations, but whether the statistical calculations made are reliable and reflect the situation in a real way is determined by the way the data is obtained and how they are analysed.

Statistics can be divided into descriptive and mathematical. As the name suggests, descriptive statistics are closely related to the description of collected data. They are primarily used to summarise a set of data and draw conclusions. Before we analyse data, we need to look at it – and this is what descriptive statistics are for.
These types of statistics can be observed when looking at data collected in tabular or graphic descriptions and are often used to determine distribution measures used to compare different groups of data – we are, of course, talking about mean, variance, median, dominance and so on.

Mathematical statistics, in contrast, is closely related to probability calculus. While descriptive statistics usually draws basic and general conclusions, mathematical statistics draw conclusions about a population from data in a given sample. For example, if we want to analyse data for Poland as a whole, we will use descriptive statistics and, for individual regions (i.e., Voivodeships), we will use mathematical statistics.

Is it worth learning how statistics work? Definitely, understanding the principles of statistics may facilitate making everyday decisions. Moreover, statistics are indispensable in many workplaces – without statistics, there would be no research on new products, no marketing or no predictions about the weather, for example. Perhaps there would be, but on what basis could they be improved? Statistics are most often used to draw conclusions and to improve or, in some way, predict the future.