Everyone in the modern world, planning to take a loan or making stocks of vegetables for the winter, periodically encounters such a concept as “average value”. Let's find out: what it is, what kinds and classes of it exist and why it is used in statistics and other disciplines.
What is the average value?
A similar name (SV) is a generalized characteristic of the totality of homogeneous phenomena, determined by any one quantitative variable.
However, people far from such abstruse definitions understand this concept as the average amount of something. For example, before taking a loan, a bank employee will definitely ask a potential client to provide data on the average income for the year, that is, the total amount of money earned by a person. It is calculated by summing the earnings for the whole year and dividing by the number of months. Thus, the bank will be able to determine whether its client will be able to repay the debt on time.
Why is it used?
As a rule, average values are widely used in order to give a final characteristic of certain social phenomena of a mass nature. They can also be used for smaller-scale calculations, as in the case of credit, in the above example.
However, most often averages are still used for global purposes. As an example of one of them, we can cite the calculation of the amount of electricity consumed by citizens during one calendar month. Based on the data obtained, maximum standards are subsequently established for categories of the population enjoying the benefits of the state.
Also, with the help of average values, the warranty service life of various household appliances, automobiles, buildings, etc. is developed. Based on the data collected in this way, modern standards of work and leisure were once developed.
In fact, any phenomenon of modern life that is massive in one way or another is necessarily associated with the concept under consideration.
Fields of application
This phenomenon is widely used in almost all exact sciences, especially those of an experimental nature.
The search for the average value is of great importance in medicine, engineering, cooking, economics, politics, etc.
Based on the data obtained from such generalizations, they develop medical preparations, training programs, establish minimum living wages and salaries, build training schedules, produce furniture, clothes and shoes, hygiene items and much more.
In mathematics, this term is called the "average value" and is used to implement solutions to various examples and problems. The simplest of them are addition and subtraction with ordinary fractions. After all, as you know, to solve such examples, it is necessary to bring both fractions to a common denominator.
Also, in the queen of exact sciences, the term “mean value of a random variable” is often used with a similar meaning. Most of it is more familiar as "mathematical expectation", more often considered in probability theory. It is worth noting that a similar phenomenon is also applied in the performance of statistical calculations.
The average value in statistics
However, most often the studied concept is used in statistics. As you know, this science in itself specializes in calculating and analyzing the quantitative characteristics of mass social phenomena. Therefore, the average value in statistics is used as a specialized method for achieving its main tasks - collecting and analyzing information.
The essence of this statistical method is to replace the individual unique values of the trait in question with a certain balanced average value.
An example is the famous joke about food. So, at a plant on Tuesdays for lunch, his superiors usually eat meat casserole, and ordinary workers - stewed cabbage. Based on these data, it can be concluded that, on average, the plant’s staff dine on stuffed cabbage on Tuesdays.
Although this example is slightly exaggerated, it illustrates the main drawback of the average search method - leveling the individual characteristics of objects or personalities.
In statistics, average data are used not only to analyze the information collected, but also to plan and predict future actions.
It also helps to evaluate the results achieved (for example, the implementation of the plan for growing and harvesting wheat for the spring-summer season).
How to calculate correctly
Although depending on the type of ST there are different formulas for calculating it, in the general theory of statistics, as a rule, only one method of calculating the average value of a feature is used. To do this, you must first add together the values of all phenomena, and then divide the resulting amount by their number.
When performing such calculations, it is worth remembering that the average value always has the same dimension (or unit of measurement) as an individual unit of the population.
Correct calculation conditions
The formula considered above is very simple and universal, so it is almost impossible to make a mistake in it. However, it is always worth considering two aspects, otherwise the obtained data will not reflect the real situation.
- Searched individual values (on the basis of which the averages are calculated) should always refer to a homogeneous population, and their number should be significant.
In the aforementioned joke, meat casserole and cabbage - belong to one category - “food”. However, if it were necessary to find out how many kilograms of cabbage are stored in the canteen of the plant, it would not make sense to take into account the meat data, since in this case they would not belong to the considered homogeneous population.
- In any individual case, it is important to take into account the qualitative content of the characteristic, the average value of which must be calculated. It is important to pay attention to the relationship between the studied characteristics and the data available for calculations.
CB classes
Having found answers to the main questions: "Average - what is this?", "Where is it used?" and “How can I calculate it?”, it is worth knowing what classes and types of NE exist.
First of all, this phenomenon is divided into 2 classes. These are structural and power average values.
Types of power NE
Each of the above classes, in turn, is divided into types. The power class has four.
- The arithmetic mean is the most common type of CB. It is the average term, in determining which the total volume of the feature in question in the aggregate of data is equally distributed between all units of this aggregate.
This type is divided into subspecies: simple and weighted arithmetic ST.
- The harmonic mean value is an indicator that is the inverse of the arithmetic mean simple, calculated from the inverse values of the feature in question.
It is used in cases where the individual values of the attribute and the product are known, but the frequency data is not.
- The geometric mean value is most often applicable when analyzing the growth rates of economic phenomena. It makes it possible to preserve unchanged the product of the individual values of a given quantity, and not the sum.
It is also simple and balanced.
- The mean square value is used in the calculation of individual indicators of indicators, such as the coefficient of variation, characterizing the rhythm of production, etc.
Also, with its help, the average diameters of pipes, wheels, the middle sides of a square and similar figures are calculated.
Like all other types of average NE, the mean square is simple and balanced.
Types of structural quantities
In addition to average NE, structural statistics are often used in statistics. They are better suited for calculating the relative characteristics of the values of a varying attribute and the internal structure of the distribution series.
There are two such species.
- Fashion. This type is most often used to determine the most popular sizes of clothes and shoes among buyers.
As a rule, the mode is calculated by such a formula.
In it, M 0 is the mode value, x 0 is the lower boundary of the modal interval, h is the size of the considered interval, f m is its frequency, f m-1 is the frequency preceding the modal interval and f m + 1 is the frequency of the next.
- The median is the value of the attribute that underlies the ranked series and dividing it into two parts, equal to each other in numerical terms.
In formulas, this type is denoted as M e .
Depending on the order in which this type of structural CB is determined (discrete or interval variational), various formulas for calculating it are used.