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BASIC PRINCIPLES OF STATISTICS - Coggle Diagram
BASIC PRINCIPLES OF STATISTICS
Introduction to Statistics
Statistics Applications
Statistics is a powerful auxiliary to many human sciences and activities: sociology, psychology, human geography, economics, and so on. It is an indispensable tool for decision making. It is also widely used to show the quantitative aspects of a situation.
Statistics is related to the process study whose result is more or less essential and in order to obtain conclusions to make reasonable decisions based on such observations.
There are many sociological or economic predictions that can be made from the exclusive application of probabilistic reasoning to objective data sets such as those of a demographic nature.
Statistics Divisions
Statistics are traditionally divided into
Inductive Statistics or Statistical Inference
Inductive Statistics or Statistical Inference
Descriptive Statistics
Those methods that include the collection, presentation and characterization of a data set in order to appropriately describe the various characteristics of that set.
History of Statistics
Simple forms of statistics have existed since the beginning of civilization, as graphical representations and other symbols were already used on skins, rocks, wooden sticks, and cave walls to count the number of people, animals, or certain things.
The Roman Empire was the first government that compiled a great amount of data on the population, surface and income of all the territories under its control.
Probability is useful for checking the reliability of statistical inferences and for predicting the type and amount of data required in a given statistical study.
What is Statistics?
Statistics is the science that studies data sets and their interpretation in mathematical terms, establishing methods for obtaining the measures that describe it, as well as for the analysis of the conclusions, with special reference to the theory of probability. It is also considered as a mathematically-based science for decision-making in the presence of uncertainty.
Data Collection and Presentation
Graphical Data Presentation - Part A
Histograms are vertical bar diagrams in which rectangular bars are constructed at the boundaries of each class.
To make the histogram, we divide the total interval of the values of the data series (from the minimum value to the maximum) into subintervals of equal amplitude that we will call classes.
Boards
Data can be collected in various ways: questionnaires, samplings, censuses, observations, and so on.
Be that as it may, after compiled, they must be summarized to facilitate their analysis. The most basic way to summarize them is through tables. Then, based on these tables, any of the following data presentation instruments can be constructed.
Frequency is the number of times the same value is repeated. The absolute frequency is presented in the table above.
Graphical Data Presentation - Part B
Pie chart
A pie or pie chart is a circle divided into parts that represent the relative frequency or percentage of the different categories.
Bar charts
In the bar graph, each category is described by a bar, the length of which represents the frequency or percentage of observations that fall into a category.
Basic concepts
Variable
Each of the traits or characteristics of the elements of a population and that vary from one individual to another (salary, eye color, sex, number of children).
Census
It is a study that is done directly to an entire population.
Individual
Each of the elements of the sample or of the population (people, screws, hospitals, shops) and on which the observation will fall.
Sampling
It is a study that is done only to a sample of the population. If the sample is representative, the results obtained will be the same or very close to those that would be obtained from taking a census.
Population
It is the set of all the elements that meet certain properties and among which it is desired to study a certain phenomenon (they can be homes, number of screws produced by a factory in a year, coin tossing, etc.). We call the statistical population or universe the reference set on which the observations will fall.
Measures of Central Tendency
Median
It is the mean value of an ordered sequence of data. If there are no ties, half of the observations will be lower and the other half will be higher. The median is not affected by extreme values. To calculate the median, you must first put the data in order. Then we use the positioning point formula.
Average or Average
The mean is an average. It is calculated by adding all the data and then dividing the total by the number of data involved. When high school students add up all their sub grades and divide them by the number of grades, they get their sub average. That average is the arithmetic mean of your partial grades.
If we have a set of data, we can calculate the mean of the set and in this way we will summarize all the information in a single number.
fashion
Definition of Central Tendency Measures
One of the most salient characteristics of the data distribution is its tendency to accumulate towards the center of it.
Those of them are:
Mean or Average (the mean value).
Median (the central value).
Fashion (the most frequent value).