The Descriptive statistics is the branch of Statistics that is responsible for collecting and organizing information about the behavior of systems with many elements, known generically by the name of population.
To do this, it uses numerical and graphic techniques, through which it presents information, without making predictions or inferences about the population from which it comes..
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Statistics has its origins in the human need to organize the information necessary for its survival and well-being, as well as to anticipate the events that affect it. The great civilizations of antiquity left records of settlers, taxes collected, amount of harvests and the size of armies.
For example, during his long reign, Ramses II (1279-1213 BC) ordered a census of lands and inhabitants in Egypt, which by then had around 2 million inhabitants.
Likewise, the Bible narrates that Moses carried out a census to find out how many soldiers the twelve tribes of Israel had.
Also in ancient Greece people and resources were counted. The Romans, notable for their high organization, periodically registered the population, drawing up censuses every five years, including territories and resources..
After the decline of Rome, important statistical records were scarce, until the arrival of the Renaissance, when Statistics resurfaces as an aid in decision-making.
At the end of the seventeenth century, the theory of probabilities was born, the result of people's inclination for games of chance, which gave Statistics the mathematical rigor that made it a science in its own right.
A new impulse came with the theory of errors and least squares in the 19th century, which was followed by the method of correlation between variables, to quantitatively assess the relationship between them..
Until finally, during the 20th century, Statistics spread to each branch of science and engineering as an indispensable tool in solving problems..
Descriptive statistics are characterized by:
- Organize the information collected in the form of data and graphs. The graphs can be diverse: histograms, frequency polygons, pie-shaped diagrams, among others..
- Distribute the data in frequency ranges to facilitate its management. Use arithmetic to find the most representative values of the data, through measures of central tendency, as well as analyze their dispersion.
- Determine the shape of the distributions, their symmetry, if they are centered or skewed, and if they are pointed or rather flattened.
Whenever data needs to be collected, organized, and presented, descriptive statistics are essential in areas of science that deal with many elements and quantities, as well as in much of human activities: economics, politics, health, sports, and more..
Here are some examples:
Descriptive statistics is concerned with consistently recording and organizing data about populations and their ages, income, investments, earnings, and expenditures. In this way, governments and institutions plan improvements and invest resources appropriately..
With its help, purchases, sales, returns and efficiency of services are monitored. For this reason, statistics are essential in decision-making.
Physics and Mechanics use Statistics to study continuous media, which consist of a large number of particles, such as atoms and molecules. It turns out that it is not possible to track each of them separately..
But studying the global behavior of the system (a portion of gas, for example) from the macroscopic point of view, it is possible to find averages and define macroscopic variables to know their properties. An example of this is the kinetic theory of gases.
It is an essential tool when monitoring diseases, from their origins and during their evolution, as well as the efficacy of treatments.
Statistics that describe morbidity rates, cure rates, incubation or development times of a disease, the age at which it usually appears, and similar data, are necessary when designing the most effective treatments..
One of the many applications of descriptive statistics is to record and order data about food consumption in different populations: its quantity, quality and which are the most consumed, among many other observations that interest experts..
Here are some examples that illustrate how useful descriptive statistics tools are to help make decisions:
The educational authorities of a country plan institutional improvements. Suppose you are going to implement a new school canteen system.
For this, it is necessary to have data about the student population, for example the number of students per grade, their age, sex, height, weight and socioeconomic status. This information is then presented in the form of tables and graphs..
To keep track of the local soccer team and make new signings, managers keep track of the number of games played, won, tied and lost, as well as the number of goals, the scorers and how they managed to score: free kick, half court, penalties, with left or right leg, among other details.
An ice cream parlor has several flavors of ice cream and wants to improve its sales, therefore the owners carry out a study where they count the number of customers, they separate them into groups by sex and age range.
In this study, the favorite ice cream flavor and the best-selling presentation are recorded, for example. And with the data collected, they plan the purchases of the flavors and the containers and accessories necessary for their preparation..
These fundamental concepts are necessary to apply statistical techniques, let's see:
In the statistical context, the population refers to the universe or group from which the information comes.
They are not always about people, since they can be groups of animals, plants or objects such as cars, atoms, molecules, and even events and ideas..
When the population is very large, a representative sample is drawn from it and analyzed, without losing relevant information..
It can be chosen at random, or according to some criteria previously established by the analyst. The advantage is that being a subset of the population, it is much more manageable.
It refers to the set of values that a certain characteristic of the population can take. A study can contain several variables, such as age, sex, weight, academic level, marital status, income, temperature, color, time and many more.
Variables can be of different nature, so there are criteria to classify them and give them the most appropriate treatment..
Depending on the way they are measured, the variables can be:
-Categorical
-Numerical
Categorical variables, also called qualitative, represent qualities such as a person's marital status, who may be single, married, divorced, or widowed.
Instead, numerical variables or quantitative, can be measured, such as age, time, weight, income and more.
Discrete variables only take discrete values, as their name implies. Examples of these are the number of children in a family, how many subjects are in a certain course and the number of cars in a parking lot.
These variables do not always take integer values, as there are also fractional ones.
On the other hand, continuous variables admit infinite values within a certain range, such as the weight of a person, the pH of the blood, the time of a telephone consultation and the diameter of soccer balls..
They give an idea of the general trend that the data is following. We will mention the three most used central measures:
-Half
-Median
-fashion
Equivalent to the average of the values. It is calculated by adding all the observations and dividing by the total number:
It is the value that is repeated the most in a data set, the most or the most frequent, since in a distribution there may be more than one mode.
When sorting a set of data, the median is the central value of all of them.
They point out the variability of the data and give an idea of how far or scattered they are from the central measures. The most used are:
It is the difference between the largest value xM and the smallest xm from a data set:
Rank = xM - xm
Measures how far the data is from the average value. For this, an average is made in turn, but with the differences between any value xi and the mean, squaring to prevent them from canceling each other out. It is usually denoted by the Greek letter σ squared, or with stwo:
The variance does not have the same units as the data, so the standard deviation is defined as the square root of the variance and is denoted as σ or s:
Instead of taking into account each data individually, it is preferable to group them into ranges, which facilitates the work, especially if there are many values. For example, when working with children in a school, they can be grouped into age ranges: 0 to 6 years, 6 to 12 years and 12 to 18 years.
They are a great way to see the distribution of the data at a glance, and contain all the information gathered in the tables and tables, but much more affordable.
There is a great variety of them: with bars, linear, circular, stem and leaf, histograms, frequency polygons and pictograms. Examples of statistical graphs are shown in Figure 3..
Branches of statistics.
Statistical variables.
Population and sample.
Inferential statistics.
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